{"id":228,"date":"2023-07-10T22:13:46","date_gmt":"2023-07-10T22:13:46","guid":{"rendered":"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/"},"modified":"2023-07-10T22:13:46","modified_gmt":"2023-07-10T22:13:46","slug":"sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/","title":{"rendered":"Sudut antara dua garis (rumus)"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan cara menghitung sudut antara dua garis (rumus). Anda juga akan dapat melihat beberapa contoh dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-angulo-entre-dos-rectas\"><\/span> Berapakah sudut antara dua garis? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> <strong>Sudut antara dua garis adalah sudut terkecil antara kedua garis tersebut.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-entre-deux-lignes-1.webp\" alt=\"sudut antara dua garis\" class=\"wp-image-1637\" width=\"225\" height=\"206\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dalam denahnya terdapat empat jenis garis tergantung pada sudut yang terbentuk di antara keduanya: garis berpotongan (antara 0\u00ba dan 90\u00ba), garis tegak lurus (90\u00ba), garis sejajar (0\u00ba) dan garis berimpit (0\u00ba). <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-143\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>garis-garis yang berpotongan<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angles-droits-secants.webp\" alt=\"sudut antara dua garis yang berpotongan\" class=\"wp-image-1644\" width=\"205\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Garis berpotongan berpotongan pada sudut lancip antara 0\u00ba dan 90\u00ba. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong><strong>Garis lurus tegak lurus<\/strong><\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-perpendiculaires-a-90-degres.webp\" alt=\"sudut antara dua garis yang tegak lurus\" class=\"wp-image-1884\" width=\"181\" height=\"207\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Garis tegak lurus berpotongan membentuk sudut siku-siku 90\u00ba. <\/p>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<div class=\"wp-block-columns is-layout-flex wp-container-146\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>Garis sejajar<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droites-paralleles-a-langle.webp\" alt=\"\" class=\"wp-image-1643\" width=\"217\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Garis sejajar tidak pernah bersentuhan dan membentuk sudut 0\u00ba di antara keduanya. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>garis yang bertepatan<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-coincident-lignes.webp\" alt=\"\" class=\"wp-image-1646\" width=\"189\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dua garis yang berhimpitan mempunyai semua titik yang sama sehingga selalu ada sudut 0\u00ba di antara keduanya.<\/p>\n<\/div>\n<\/div>\n<p> Kesimpulannya, perhitungan sudut antara dua garis sejajar, berimpit, atau tegak lurus adalah langsung: garis sejajar dan garis berimpit membentuk sudut 0 derajat karena arahnya sama, dan garis tegak lurus tersebut berpotongan dengan sudut 90 derajat. . Sebaliknya, untuk mencari sudut antara dua garis yang berpotongan, Anda harus menerapkan rumus (kita akan melihatnya di bawah). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-el-angulo-entre-dos-rectas\"><\/span> Bagaimana cara menghitung sudut antara dua garis? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Ada dua cara untuk menghitung sudut antara dua garis. Cara pertama menggunakan <strong>vektor arah<\/strong> setiap garis dan cara kedua berdasarkan <strong>kemiringan<\/strong> setiap garis.<\/p>\n<p> Tidak ada prosedur yang lebih baik dari yang lain, pada kenyataannya keduanya cukup mudah, namun bergantung pada bagaimana garis-garis tersebut diungkapkan, satu metode atau lainnya praktis. Oleh karena itu kami menyarankan Anda mengetahui cara menggunakan kedua metode matematika tersebut. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"metodo-de-los-vectores-directores-de-las-rectas\"><\/span> Metode orientasi vektor garis<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Rumus menghitung sudut antara dua garis dengan menggunakan vektor arahnya adalah: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Diketahui vektor arah dari dua garis yang berbeda:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b626c82ac04d69ba3bcafb5fa87d7d00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (\\text{u}_x,\\text{u}_y)\\qquad \\vv{\\text{v}} = (\\text{v}_x,\\text{v}_y)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"216\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Sudut antara kedua garis tersebut dapat dihitung dengan rumus berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19eb97a6cf27fffc3ea832e388f924a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert \\vv{\\text{u}} \\cdot \\vv{\\text{v}}\\rvert}{\\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"127\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4501274336c637b37c6332eae5c6c229_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"16\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a59cd4f2581db3318d38a2a77340a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah modul dari vektor<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> masing-masing.<\/p>\n<\/div>\n<p> Ingatlah bahwa rumus besar suatu vektor adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0761a6a31d273eefccceb4aad7556a6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{\\text{v}} \\rvert = \\sqrt{ \\text{v}_x^2+\\text{v}_y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"117\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p> Mari kita lihat cara mencari sudut antara dua garis dengan contoh:<\/p>\n<ul>\n<li> Hitunglah sudut antara dua garis berikut: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a336a6cbbd7581f1fb6481561aef1efc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=2-3t \\\\[2ex]y=1+4t \\end{cases} \\qquad s: \\ 2x-5y+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"334\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Untuk menghitung sudut antara dua garis, Anda harus terlebih dahulu mencari vektor arah setiap garis.<\/p>\n<p> hak<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dinyatakan dalam bentuk <a href=\"https:\/\/mathority.org\/id\/rumus-persamaan-parametrik-suatu-garis\/\">persamaan parametrik<\/a> , maka komponen vektor yang menandai arahnya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d3e98a6c4a49b9b38e463795eb44b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-3,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> dan hukum<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea93feaa2c7157ec666d9a59c0f6a699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> didefinisikan dalam bentuk persamaan implisit (atau umum), sehingga koordinat vektor arahnya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25fa1b333fb55fd35e2ff773a99aab2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (-B,A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59f221044ed855cbee5120d8936cc247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang setelah kita mengetahui vektor arah setiap garis, kita dapat menggunakan rumus sudut antara dua garis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kita tentukan besar kedua vektor tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5630e1894a54b931779a240cce2b3460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{(-3)^2+4^2}= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"172\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b8dca924b988372d9cc00e5a3e79041_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{5^2+2^2}= \\sqrt{29}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kami melakukan operasi vektor dari rumus sudut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f1810380fc6ddab753a49fb43d8d136_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(-3,4) \\cdot (5,2)\\rvert}{5 \\cdot \\sqrt{29}}= \\cfrac{\\lvert-3 \\cdot 5 + 4\\cdot 2\\rvert}{26,93} = \\cfrac{7}{26,93} = 0,26\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"449\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Dan terakhir, kita menghitung sudut yang dibentuk oleh dua garis dengan kebalikan kosinus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-839ce1333f41e5392ef7d2127853aae2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,26) = \\bm{74,93\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa Anda dapat menghitung invers kosinus menggunakan kalkulator dengan kuncinya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b70d14d21b828bcf46c4104f901c916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{\\cos ^{-1}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"57\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"metodo-de-las-pendientes\"><\/span> metode kemiringan<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Tentunya untuk memahami cara ini, Anda perlu mengetahui <a href=\"https:\/\/mathority.org\/id\/kemiringan-rumus-garis\/\">kemiringan garis<\/a> . Anda dapat meninjau konsep ini di tautan, di mana Anda akan menemukan penjelasan rinci tentang artinya, cara menghitungnya, contoh dan latihan penyelesaian kemiringan suatu garis.<\/p>\n<p> Rumus menghitung sudut antara dua garis dari lerengnya adalah: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Atau dua baris berbeda:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9768adb30eaa8e08b67c58e5c4921df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_1 : \\ y=m_1 x+n_1 \\qquad r_2: \\ y=m_2 x+n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"321\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Sudut antara kedua garis tersebut dapat ditentukan dengan rumus berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82acfc9ae51ee3a469cfabc7024aa75c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_2-m_1}{1+m_1\\cdot m_2} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"166\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-51921237944fd6e43f0640228a37376f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"22\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6dae86895dac0d4644151786b47c7ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah kemiringan garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6ce00e1b287bac058a29aa4a5cc2b715_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80681c4f8159fb897fed760530a2ef01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> masing-masing.<\/p>\n<\/div>\n<p> Mari kita lihat cara menghitung sudut antara dua garis menggunakan kemiringannya dengan contoh:<\/p>\n<ul>\n<li> Tentukan sudut antara dua garis berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37af9568ead27bf5cc0bedd4e23107b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=4x-2 \\qquad s: \\ y=-3x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"272\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Kemiringan setiap garis adalah angka sebelum variabel <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-845f2902b8bebf60c3c7372a7fbe4d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6fd143f62c08661d4c17431b128bdcf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a6063973129bb0bac4b98714e474f8ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_s = -3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, sudut antara dua garis dapat dicari dengan menggunakan rumus kemiringan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-639af21616a579864711c6c3466a5157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{-3-4}{1+4\\cdot (-3)} \\end{vmatrix}=\\begin{vmatrix} \\cfrac{-7}{-11} \\end{vmatrix} = 0,64\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"294\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p> Dan akhirnya kita menemukan sudut dengan kebalikan dari garis singgung:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-caed83d6028d223b06c41f639e5323e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{tg}^{-1}(0,64) = \\bm{32,62\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa Anda dapat menghitung kebalikan dari garis singgung menggunakan kalkulator dengan kuncinya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2be52d0cf4b9ef4f831429feec90b416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{\\tan ^{-1}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"59\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Kita baru saja melihat contoh kemiringan dua garis yang dinyatakan sebagai persamaan eksplisit, namun jika keduanya berbentuk <a href=\"https:\/\/mathority.org\/id\/persamaan-titik-kemiringan-rumus-garis\/\">persamaan kemiringan titik,<\/a> prosedur yang sama harus digunakan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-angulos-entre-dos-rectas\"><\/span> Menyelesaikan masalah sudut antara dua garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan sudut yang dibentuk oleh dua garis berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-975bcacc5eecede0a2288a39eeb27a73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=4+t \\\\[2ex]y=-3-2t \\end{cases} \\qquad s: \\ \\begin{cases} x=4t \\\\[2ex]y=-1-t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"324\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam hal ini kita akan menggunakan metode vektor arah. Oleh karena itu, kita harus mencari terlebih dahulu vektor arah setiap garis. Kedua garis tersebut dinyatakan sebagai persamaan parametrik, sehingga komponen vektor arahnya adalah suku di depan parameternya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ac0191cf7cbec493c10a4fa8197e2a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97225ee00d3957d5d85cdc93c8015ed4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang setelah kita mengetahui vektor arah setiap garis, kita dapat menggunakan rumus sudut antara dua garis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita tentukan besar kedua vektor tersebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2e501df610a9ae606c598ec472017f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{1^2+(-2)^2}= \\sqrt{5}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"187\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9e23805a7bdb58bd0b4893d4b6e586a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{4^2+(-1)^2}= \\sqrt{17}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikan produk skalar antara dua vektor pembilang dan perkalian modul penyebut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e5d926125129db13c541515e1dd0beba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(1,-2) \\cdot (4,-1)\\rvert}{\\sqrt{5} \\cdot \\sqrt{17}}= \\cfrac{\\lvert 1 \\cdot 4 + (-2)\\cdot (-1)\\rvert}{9,22} = \\cfrac{6}{9,22} = 0,65\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"494\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita mencari sudut yang dibentuk oleh dua garis dengan melakukan invers kosinus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ede88ebdcf81c8914fed546ba2a0d1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,65) = \\bm{49,40\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Tentukan sudut antara dua garis berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-818fae5a2074424ec782243f26c5708c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ -3x+4y+1=0 \\qquad s: \\ \\cfrac{x-1}{6} = \\cfrac{y+5}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"337\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kita akan menyelesaikan soal ini dengan menggunakan metode vektor arah, jadi pertama-tama kita perlu mencari vektor arah setiap garis. hak<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dinyatakan dalam bentuk persamaan umum (atau implisit), sehingga komponen vektor yang menandai arahnya adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-381327f58ef6c881ed34e78624c91b8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-B,A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-383a5264ab7ded87d5684560e6263e15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} = (-4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> dan hukum<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ea93feaa2c7157ec666d9a59c0f6a699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> didefinisikan dalam bentuk persamaan kontinu, sehingga koordinat kartesius vektor arahnya adalah bilangan penyebutnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ba6fe3a3d80f3a44c2c3a0c8345ffa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} = (6,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui vektor arah setiap garis, kita dapat menggunakan rumus sudut antara dua garis:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menentukan modul dari dua vektor: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-565377b63a2e28ce9613745bc0c0b756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{r} \\rvert = \\sqrt{(-4)^2+(-3)^2}= 5\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65100d7dbdf97aa72e9212379ff54de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lvert \\vv{s} \\rvert = \\sqrt{6^2+3^2}= \\sqrt{45}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami melakukan operasi antar vektor dengan rumus sudut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-790804eb21bd7b19771c5597b3cea577_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert\\vv{r} \\cdot \\vv{s}\\rvert}{\\lvert \\vv{r} \\rvert \\cdot \\lvert \\vv{s} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"125\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a36b58fc65b59f20656acc68016020ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cos(\\alpha) =\\cfrac{\\lvert(-4,-3) \\cdot (6,3)\\rvert}{5 \\cdot \\sqrt{45}}= \\cfrac{\\lvert -4 \\cdot 6 + (-3)\\cdot 3\\rvert}{33,54} = \\cfrac{33}{33,54} = 0,98\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"490\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita menghitung sudut yang dibentuk oleh dua garis dengan kebalikan kosinus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-216ef184adb4e8e26ea4dba3a0d41a67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{cos}^{-1}(0,98) = \\bm{10,30\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Berapakah sudut antara dua garis berikut? <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3a559370fd832ad2f4707782cf40cb37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=-2x+9 \\qquad s: \\ y=5x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"272\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam hal ini, kita akan menggunakan metode kemiringan garis untuk mengetahui sudut yang dibentuknya, karena garis-garis tersebut berbentuk persamaan eksplisit.<\/p>\n<p class=\"has-text-align-left\"> Kemiringan setiap garis merupakan bilangan yang menyertai variabel bebas <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-845f2902b8bebf60c3c7372a7fbe4d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42a36a89145f23919d8665908c3e2bc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42de98336b7cbc2dc475ea3037bebc55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_s = 5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, sudut antara kedua garis dapat ditentukan dengan menggunakan rumus kemiringan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-172bd34124a3b9e86696158d992eebb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{-2-5}{1+5\\cdot (-2)} \\end{vmatrix}=\\begin{vmatrix} \\cfrac{-7}{-9} \\end{vmatrix} = 0,78\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"293\" style=\"vertical-align: -19px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir kita mencari sudut antara dua garis dengan membalik garis singgungnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c84b4105875a851c576fb326e2ba6f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha= \\text{tg}^{-1}(0,78) = \\bm{37,87\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Temukan persamaan garis yang melalui titik tersebut<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6958f848b3f39930bc315b56f627f888_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(5,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan membentuk sudut 45\u00ba dengan garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dikatakan baris: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34edcc0a8f3b1c557be083882ab8b7e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ y=2x+4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"112\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengatasi masalah ini, kami akan menelepon<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> ke kanan yang akan kita hitung. Selain itu, kita akan menggunakan metode kemiringan karena kita mengetahui kemiringan garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9edd8ad155030a560ef8313513b5ac14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dari rumus sudut antara dua garis (metode kemiringan) kita dapat memperoleh nilai kemiringan garis <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-580a84fe09f12aa20c352a8336880e41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-551288f526b75201969ebf9117fc9b1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(\\alpha) =\\begin{vmatrix} \\cfrac{m_s-m_r}{1+m_r\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"165\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami mengganti nilai yang diketahui ke dalam rumus:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ace7fdfc7474a43a6fad81e0185d0050_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{tg}(45\u00ba) =\\begin{vmatrix} \\cfrac{m_s-2}{1+2\\cdot m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami mencoba menyelesaikan persamaan yang dihasilkan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0f2ea68d68e24c3e30df526dfb88873c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =\\begin{vmatrix} \\cfrac{m_s-2}{1+2m_s} \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"105\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Nilai absolut persamaan membuatnya agak sulit untuk diselesaikan, karena Anda harus menganalisis opsi positif dan negatif: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-149\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ad2ad90ee94f08746cea11db3a6917f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =+\\cfrac{m_s-2}{1+2m_s}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"110\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56c4a065c3919fbe023153fe2ba9133c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 \\cdot (1+2m_s)=m_s-2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"173\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d31fa5d4b608e062c0e15476b3f15e7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1+2m_s=m_s-2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"137\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-870381f6e915e33b32ad147c9a4de5fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2m_s-m_s=-2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"152\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1d7c13f0d7d21af8c407f7f535e0d994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m_s=-3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b9e6f5eb952e8ea9758af5497ed8cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 =-\\cfrac{m_s-2}{1+2m_s}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"110\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b984c3bc74269597752a909f457c8ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1 \\cdot (1+2m_s)=-(m_s-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df53d7b057ec0e6b6f7701fb5149cbe0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 1+2m_s=-m_s+2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"151\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a96107cb59f52dcf9bb703e54c27757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2m_s+m_s=2-1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"138\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-067dac6d6aea31f65caccf5ed9c30052_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 3m_s=1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9003dbf8679e5b0aaa8c10777f6d38fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle m_s=\\cfrac{1}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"57\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Oleh karena itu kita mempunyai dua kemungkinan solusi: sebuah garis dengan kemiringan -3 dan garis lainnya dengan kemiringan sepertiga.<\/p>\n<p class=\"has-text-align-left\"> Rumus persamaan titik-kemiringan suatu garis adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3441e1da8c7da5805b1133af77b14f60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, setelah kita mengetahui kemiringan kedua garis yang mungkin terjadi, kita dapat menuliskan persamaan titik-kemiringan setiap garis dengan titik yang harus dilaluinya sesuai dengan pernyataan, <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c8726fb72614f7e8f7e546f9ac6995cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(5,-1):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a69157a1cf6a00b750b804590e63524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s: \\ y+1=-3(x-5) \\qquad \\qquad s': \\ y+1=\\cfrac{1}{3}(x-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"402\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan cara menghitung sudut antara dua garis (rumus). Anda juga akan dapat melihat beberapa contoh dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Berapakah sudut antara dua garis? Sudut antara dua garis adalah sudut terkecil antara kedua garis tersebut. Dalam denahnya terdapat empat &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\"> <span class=\"screen-reader-text\">Sudut antara dua garis (rumus)<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[47],"tags":[],"class_list":["post-228","post","type-post","status-publish","format-standard","hentry","category-titik-garis-dan-bidang"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sudut antara dua garis (rumus) - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sudut antara dua garis (rumus) - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan penjelasan cara menghitung sudut antara dua garis (rumus). Anda juga akan dapat melihat beberapa contoh dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Berapakah sudut antara dua garis? Sudut antara dua garis adalah sudut terkecil antara kedua garis tersebut. Dalam denahnya terdapat empat &hellip; Sudut antara dua garis (rumus) Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T22:13:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-entre-deux-lignes-1.webp\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Sudut antara dua garis (rumus)\",\"datePublished\":\"2023-07-10T22:13:46+00:00\",\"dateModified\":\"2023-07-10T22:13:46+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\"},\"wordCount\":983,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Titik, garis, dan bidang\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\",\"url\":\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\",\"name\":\"Sudut antara dua garis (rumus) - 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