{"id":271,"date":"2023-07-10T01:20:15","date_gmt":"2023-07-10T01:20:15","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-rumus-sudut-antara-garis-dan-bidang-serta-latihan-soalnya\/"},"modified":"2023-07-10T01:20:15","modified_gmt":"2023-07-10T01:20:15","slug":"contoh-rumus-sudut-antara-garis-dan-bidang-serta-latihan-soalnya","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-rumus-sudut-antara-garis-dan-bidang-serta-latihan-soalnya\/","title":{"rendered":"Sudut antara garis dan bidang"},"content":{"rendered":"<p>Di sini Anda akan menemukan cara menghitung sudut antara garis dan bidang. Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan yang diselesaikan langkah demi langkah tentang sudut antara garis dan bidang. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-el-angulo-entre-una-recta-y-un-plano\"><\/span> Berapakah sudut antara garis dan bidang?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sudut antara garis dan bidang adalah sudut antara garis dan proyeksi ortogonalnya pada bidang tersebut. <\/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-une-ligne-et-un-plan.webp\" alt=\"Berapakah sudut antara garis dan bidang?\" class=\"wp-image-3943\" width=\"500\" height=\"283\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Sudut antara suatu garis dan suatu bidang merupakan komplemen dari sudut antara garis tersebut dengan vektor tegak lurus bidang tersebut. Oleh karena itu, sudut antara garis dan bidang dihitung dari sudut antara vektor arah garis dan vektor normal bidang tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-angulo-entre-una-recta-y-un-plano\"><\/span> Rumus sudut antara garis dan bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk menyimpulkan rumus sudut antara bidang dan garis, Anda perlu mengetahui cara <a href=\"https:\/\/mathority.org\/id\/cara-menghitung-sudut-antara-dua-vektor-contoh-latihan-yang-diselesaikan\/\">mencari sudut antara dua vektor<\/a> . Di halaman tertaut Anda akan menemukan penjelasan serta contoh dan latihan yang diselesaikan langkah demi langkah, jadi jika Anda tidak ingat cara melakukannya, kami sarankan Anda melihatnya.<\/p>\n<p> Jadi, karena sudut antara garis dan bidang berkomplemen dengan sudut antara vektor arah garis 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-e01bc8353ce87c4e409251c9a78dae8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}_r)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"29\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan vektor normal terhadap bidang tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-45cf5bc44c73892962f2e851f74daacc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{n})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p> , dari rumus sudut antara dua vektor kita menyimpulkan bahwa sudut antara garis dan bidang ekuivalen dengan persamaan 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-432b11c5cc73074467112392e29b46ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)=\\cos(90-\\alpha) =\\cfrac{\\lvert \\vv{\\text{v}}_r \\cdot \\vv{n} \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"247\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi, <strong>rumus sudut antara garis dan bidang adalah<\/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-une-droite-et-un-plan-formule.webp\" alt=\"sudut antara garis dan bidang rumus\" class=\"wp-image-3975\" width=\"282\" height=\"132\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50f32076ae1ee85f5b7c5a6d43a03089_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah vektor langsung dari garis tersebut.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-10affe1faee06a5faa4ef6d9c0473b1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah vektor normal terhadap bidang. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-el-angulo-entre-una-recta-y-un-plano\"><\/span> Contoh menghitung sudut antara garis dan bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agar Anda dapat mengetahui cara menyelesaikan soal seperti ini, berikut adalah contoh menghitung sudut antara garis dan bidang:<\/p>\n<ul>\n<li> Hitunglah sudut yang dibentuk oleh garis tersebut\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> dengan pesawat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> Biarkan persamaannya menjadi:<\/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-cb8b61cb99a7af826a63ee098efc3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x= 3-t \\\\[1.7ex] y = 2+4t \\\\[1.7ex] z=-3t \\end{cases}\\qquad\\qquad \\pi : \\ x-y+4z+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"392\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Garis tersebut dinyatakan dalam bentuk persamaan parametrik, sehingga 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-f5c132cae76c4e7d2eef34b80dda60e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-1,4,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebaliknya, bidang didefinisikan dalam bentuk persamaan implisit (atau umum), sehingga vektor normalnya 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-6c8001623f05fee4f3266c426e184482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (1,-1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jadi, setelah kita mengetahui vektor arah garis dan vektor normal bidang, kita terapkan rumus sudut antara garis dan bidang:<\/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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Kami mengganti vektor 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-60faf9957c871b9c9e62fe4ffc9b6973_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-1,4,-3) \\cdot (1,-1,4)\\rvert}{\\sqrt{(-1)^2+4^2+(-3)^2} \\cdot \\sqrt{1^2+(-1)^2+4^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"393\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Dan kami melakukan perhitungan: <\/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-ecf6e128745b2cea94a0651a086d9708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -1\\cdot 1 +4 \\cdot (-1) + (-3) \\cdot 4\\rvert}{\\sqrt{26}\\cdot \\sqrt{18}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"289\" style=\"vertical-align: -16px;\"><\/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-d9ddce2ff5d93699f7583e541c33126d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-17|}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"125\" style=\"vertical-align: -16px;\"><\/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-df350eb37802b9a0fd712299478ece35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{17}{\\sqrt{468}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"117\" style=\"vertical-align: -16px;\"><\/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-77b7a2aaf4989013b48a34274af4b246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,79\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Terakhir, kita membalikkan sinus dengan kalkulator dan mencari nilai 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-4222f5a3e1dc32c123215c725dffadcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,79) = \\bm{51,80\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, sudut antara garis dan bidang kira-kira 51,80\u00ba.<\/p>\n<p> Kita harus ingat bahwa jika kita memperoleh hasil 0\u00ba, berarti garis dan bidang sejajar atau garis tersebut terdapat di dalam bidang. Dan jika sudutnya sama dengan 90\u00ba, berarti garis dan bidang tersebut tegak lurus. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-angulo-entre-una-recta-y-un-plano\"><\/span>Menyelesaikan masalah sudut antara garis dan bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Temukan sudut yang dibentuk oleh 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-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> dengan pesawat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> Biarkan persamaannya menjadi: <\/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-187a958fc02bef31b18b2c2f95379015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\cfrac{x-1}{2} = \\cfrac{y+1}{-1} = \\cfrac{z+3}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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-97968f3ad3bc2327d83f308575a4607d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 3x+y+2z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"184\" 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\"> Garis tersebut dinyatakan sebagai persamaan kontinu, sehingga 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-ce8d892f9706e946ee38bea5601f420c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (2,-1,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya, bidang tersebut berbentuk persamaan implisit (atau umum), sehingga vektor normalnya 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-d9b2fb6c5a45dd5cff0e5c949ab7ee22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, setelah kita mengetahui vektor arah garis dan vektor normal bidang, kita menggunakan rumus sudut antara garis dan bidang: <\/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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" 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-f79b0514974ecd648d402afe09fce215_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(2,-1,-3) \\cdot (3,1,2)\\rvert}{\\sqrt{2^2+(-1)^2+(-3)^2} \\cdot \\sqrt{3^2+1^2+2^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"362\" style=\"vertical-align: -20px;\"><\/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-43b3452fc0559594f81d5793eb69bd50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert 2\\cdot 3 +(-1) \\cdot 1 + (-3) \\cdot 2\\rvert}{\\sqrt{14}\\cdot \\sqrt{14}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"275\" style=\"vertical-align: -16px;\"><\/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-0fae771d5c74fc70f8c235e7d977b97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{|-1|}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"116\" style=\"vertical-align: -12px;\"><\/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-4af96594105dfe56eb0b48a782596cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{1}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" style=\"vertical-align: -12px;\"><\/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-c26a8cbca5ca49005ddf750822a16359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,07\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kita balikkan sinus dan cari nilai sudutnya:<\/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-6280b70e3e9db10239c8ed41338921b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,07) = \\bm{4,10\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"185\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, sudut antara garis dan bidang adalah 4,10\u00ba.<\/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 yang dibentuk oleh garis 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-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> dengan pesawat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26622dd58bf71cd1b543c3d83233c561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> Biarkan persamaannya menjadi: <\/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-6a8165b8e50fbc7764c77d1a984de353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} 3x-y+4z+1=0 \\\\[2ex] x+2y-2z+6=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"198\" 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-4ef4dec995f97607a7e037e37eeb0b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ -4x+2y-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"167\" 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\"> Garis dinyatakan dengan persamaan implisit (atau umum), oleh karena itu perlu mencari vektor arah garis dengan menghitung hasil kali vektor dari vektor-vektor yang tegak lurus pada 2 bidang yang menentukan 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-54cc86087728e7e163034c95afc55286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -1 &amp; 4 \\\\[1.1ex] 1 &amp;2&amp;-2 \\end{vmatrix}  = -6\\vv{i}+10\\vv{j}+7\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"236\" 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-d96017e2fa07a08307c10dc57ee61c8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (-6,10,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya, vektor normal bidang 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-029b4c2fd253e26ab1b4c273507b5527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (-4,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, setelah kita mengetahui vektor arah garis dan vektor normal bidang, kita menggunakan rumus sudut antara garis dan bidang: <\/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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" 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-dc066db1739212edabe5d565f906830b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sen}(\\alpha) =\\cfrac{\\lvert(-6,10,7) \\cdot (-4,2,0)\\rvert}{\\sqrt{(-6)^2+10^2+7^2} \\cdot \\sqrt{(-4)^2+2^2+0^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"374\" style=\"vertical-align: -20px;\"><\/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-d143bdbebf8285d4543063a31d886c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)  =\\cfrac{\\lvert -6\\cdot (-4) +10 \\cdot 2 + 7 \\cdot 0\\rvert}{\\sqrt{185}\\cdot \\sqrt{20}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"271\" style=\"vertical-align: -16px;\"><\/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-35ceee51406f9d5bcc316b74690eb299_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) = \\cfrac{44}{\\sqrt{3700}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"126\" style=\"vertical-align: -16px;\"><\/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-84549d70edc1d856e90c75ec50421389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha)= 0,72\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Terakhir, kita balikkan sinus dan cari nilai sudutnya:<\/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-e843d4cbca4933f7ba383adcd6566028_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha = \\text{sen}^{-1} (0,72) = \\bm{46,33\u00ba}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"194\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, sudut antara garis dan bidang adalah 46,33\u00ba.<\/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> Tentukan, dengan menggunakan rumus sudut antara garis dan bidang, nilai<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> diperlukan untuk hak<\/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> dan pesawat<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> menjadi paralel. <\/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-5ce940060c57c2eae41e79fb31db1afe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ (x,y,z) = (2,0-1)+t(4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" 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-2f733e6dda28d7a2ab79930a2e311d76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\pi : \\ 4x+3y+kz+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"194\" 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\"> Pertama, garis dinyatakan sebagai persamaan vektor, sehingga 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-d80ac01e619cde85001850e17e3f2bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r = (4,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya bidang tersebut berbentuk persamaan umum, sehingga vektor normalnya 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-b4a7ab8f96745e213fbc290625f5b463_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{n} = (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, agar dua elemen geometri sejajar, sudut antara keduanya harus nol. Jadi, rumus sudut antara garis dan bidang 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-5cb21d7d0053f3ffb4a8d0b19e824495_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(\\alpha) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"135\" 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-efc7281925b7c514913e4aaf9102d342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{sen}(0\u00ba) =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"133\" 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-240cba5c3a27806488b1e8172b55b8a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\cfrac{\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"94\" 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-61e18ce576fafff8b4db05f6bca9cedb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 \\cdot \\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{n} \\rvert =\\lvert\\vv{\\text{v}}_r \\cdot \\vv{n}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" 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-4639b105473c348e32b6d87593e0ab31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =\\vv{\\text{v}}_r \\cdot \\vv{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, perkalian titik antara vektor arah garis dan vektor normal harus sama dengan nol. Dan dari persamaan ini kita dapat menentukan nilai yang tidak diketahui <\/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-7cf6d2c84f82625cb8a795ee1394251f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" 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-7dd4a6abbc2ab11fe54f43b6aeea5ee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =(4,-1,3) \\cdot (4,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" 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-ecedbfc73f2ae09aa2f20d886b76217a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =4\\cdot 4 -1\\cdot 3 +3 \\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"168\" style=\"vertical-align: -2px;\"><\/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-d6b2fc367d696e22656777d9c8394f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 0 =16 -3 +3 k\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"120\" style=\"vertical-align: -2px;\"><\/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-14bd0daaa168493c0978bdec5f548829_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -3k =13\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" 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-27a35752a178021d706238eff36fe7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k =\\cfrac{13}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"58\" style=\"vertical-align: -12px;\"><\/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-0aef8d9f84e0eeb1eceb52873846ca57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k =-}\\mathbf{\\cfrac{13}{3}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"70\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Terakhir, jika artikel ini bermanfaat bagi Anda, Anda mungkin juga tertarik dengan cara mencari <a href=\"https:\/\/mathority.org\/id\/sudut-antara-dua-bidang-dalam-rumus-ruang-r3\/\">sudut antara dua bidang<\/a> . Pada halaman link anda akan menemukan penjelasan yang sangat detail serta rumus yang diperlukan untuk menghitung sudut antara dua bidang yang berbeda dan, sebagai tambahan, anda akan dapat melihat contoh dan latihan yang diselesaikan selangkah demi selangkah untuk dapat berlatih dan memahami. bagaimana hal itu dilakukan dengan sempurna.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan cara menghitung sudut antara garis dan bidang. Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan yang diselesaikan langkah demi langkah tentang sudut antara garis dan bidang. Berapakah sudut antara garis dan bidang? Sudut antara garis dan bidang adalah sudut antara garis dan proyeksi ortogonalnya pada bidang &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-rumus-sudut-antara-garis-dan-bidang-serta-latihan-soalnya\/\"> <span class=\"screen-reader-text\">Sudut antara garis dan bidang<\/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-271","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 garis dan bidang - 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\/contoh-rumus-sudut-antara-garis-dan-bidang-serta-latihan-soalnya\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sudut antara garis dan bidang - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan cara menghitung sudut antara garis dan bidang. Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan yang diselesaikan langkah demi langkah tentang sudut antara garis dan bidang. Berapakah sudut antara garis dan bidang? 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