{"id":10408,"date":"2018-02-28T10:27:24","date_gmt":"2018-02-28T03:27:24","guid":{"rendered":"https:\/\/example.com\/?p=10408"},"modified":"2023-10-22T22:55:57","modified_gmt":"2023-10-22T15:55:57","slug":"apa-itu-aturan-sinus-dan-cosinus","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus","title":{"rendered":"Apa Itu Aturan Sinus dan Cosinus? | Matematika Kelas 10"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Header%20blog%20RG\/Matematika_10.jpg\" alt=\"Matematika_10.jpg\" style=\"display: block; margin-left: auto; margin-right: auto; width: 820px;\" title=\"Matematika_10.jpg\" width=\"820\" caption=\"false\" data-constrained=\"true\"><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Squad, kamu pasti sudah tidak asing lagi dengan kata sinus dan cosinus, bukan?&nbsp;Dalam trigonometri, ternyata sinus dan cosinus mempunyai aturan tersendiri, khususnya pada segitiga. Apa itu aturannya? Perbandingan panjang sisi dengan sudut pada segitiga serta menghitung luas segitiga dilakukan dengan menggunakan prinsip trigonometri. Untuk penjelasan selengkapnya, simak di bawah ini ya.<\/span><\/p>\n<p><!--more--><\/p>\n<h3 style=\"text-align: justify;\"><span style=\"color: #3366ff; font-size: 20px;\"><strong>Aturan Sinus<\/strong><\/span><\/h3>\n<p style=\"text-align: justify;\"><span><strong>Menjelaskan hubungan antara perbandingan panjang sisi yang berhadapan dengan sudut terhadap sinus sudut pada segitiga.<\/strong> Berdasarkan aturan sinus dalam segitiga ABC, perbandingan panjang sisi dengan sinus sudut yang berhadapan dengan sisi segitiga mempunyai nilai yang sama.<\/span> Seperti yang dijelaskan pada gambar di bawah ini.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/aturan%20sinus-1.png\" alt=\"sinus dan cosinus\" style=\"display: block; margin-left: auto; margin-right: auto; width: 400px;\" title=\"sinus dan cosinus\" width=\"400\" caption=\"false\" data-constrained=\"true\">Segitiga sembarang \u0394 ABC<\/p>\n<p style=\"text-align: left;\">Keterangan:<\/p>\n<p style=\"text-align: left;\">a = panjang sisi a<\/p>\n<p style=\"text-align: left;\">A = besar sudut di hadapan sisi a<\/p>\n<p style=\"text-align: left;\">b = panjang sisi b<\/p>\n<p style=\"text-align: left;\">B = besar sudut di hadapan sisi b<\/p>\n<p style=\"text-align: left;\">c = panjang sisi c<\/p>\n<p style=\"text-align: left;\">C = besar sudut di hadapan sisi c<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/sinus.png\" alt=\"sinus.png\" style=\"width: 436px; margin: 0px 10px 10px 0px; float: left;\" width=\"436\"><\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">Supaya kamu lebih paham, kerjakan <strong>contoh soal<\/strong> di bawah ini <em>yuk<\/em> Squad!<\/div>\n<ul style=\"list-style-type: circle;\">\n<li style=\"text-align: justify;\">Sebuah segitiga diketahui memiliki sudut A = 30\u00ba, sisi a = 3 dan sisi b = 4. Hitung besar sudut B, besar sudut C dan panjang sisi c!<\/li>\n<\/ul>\n<p><strong>Diketahui:<\/strong><\/p>\n<p>A = 30\u00ba<\/p>\n<p>a = 3<\/p>\n<p>b = 4<\/p>\n<p><strong>Ditanya:<\/strong> B, C dan c?<\/p>\n<p><strong>Jawab:<\/strong><\/p>\n<ul style=\"list-style-type: disc;\">\n<li>Menentukan besar sudut B<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/soal%20sinus.png\" alt=\"soal sinus.png\" style=\"width: 433px;\"><\/p>\n<p>Karena sinus harus bernilai positif baik di kuadran I maupun kuadran II, maka sudut lain yang memenuhi adalah B = (180\u00ba &#8211; 41,8\u00ba) = 138,2\u00ba<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>Menentukan besar sudut C<\/li>\n<\/ul>\n<p>Jumlah sudut-sudut dalam segitiga adalah 180\u00ba, oleh karena itu berlaku:<\/p>\n<p>A + B + C = 180\u00ba \u2192 C = 180\u00ba &#8211; (A + B)<\/p>\n<p>Untuk B = 41,8\u00ba \u2192 C = 180\u00ba &#8211; (30\u00ba + 41,8\u00ba) = 108,2\u00ba<\/p>\n<p>Untuk B = 138,2\u00ba \u2192 C = 180\u00ba &#8211; (30\u00ba + 138,2\u00ba) = 11,8\u00ba<\/p>\n<ul style=\"list-style-type: disc;\">\n<li>Menentukan panjang sisi C<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/sinusss.png\" alt=\"sinusss.png\" style=\"width: 305px;\"><\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: justify;\"><span style=\"color: #3366ff; font-size: 20px;\"><strong style=\"background-color: transparent;\">Aturan Cosinus<\/strong><\/span><\/div>\n<p style=\"text-align: justify;\"><strong>Aturan Cosinus merupakan aturan yang menjelaskan hubungan antara kuadrat panjang sisi dengan nilai cosinus dari salah satu sudut pada segitiga.&nbsp;<\/strong>Aturan cosinus dapat digunakan untuk menentukan unsur-unsur lain dalam suatu segitiga sembarang untuk dua kasus yaitu saat tiga sisi ketahui dan saat dua sisi dan sudut apitnya diketahui. Seperti&nbsp;yang dijelaskan pada gambar di bawah ini.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/cosinus.png\" alt=\"cosinus.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"><\/p>\n<p style=\"text-align: center;\">Segitiga sembarang \u0394 ABC<\/p>\n<p style=\"text-align: left;\">Keterangan:<\/p>\n<p style=\"text-align: left;\">a = panjang sisi a<\/p>\n<p style=\"text-align: left;\">A = besar sudut di hadapan sisi a<\/p>\n<p style=\"text-align: left;\">b = panjang sisi b<\/p>\n<p style=\"text-align: left;\">B = besar sudut di hadapan sisi b<\/p>\n<p style=\"text-align: left;\">c = panjang sisi c<\/p>\n<p style=\"text-align: left;\">C = besar sudut di hadapan sisi c<\/p>\n<div style=\"text-align: justify;\"><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Beasiswa%20Page%20Assets\/cosinuss.png\" alt=\"cosinuss.png\" style=\"width: 370px;\"><\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">Sehingga aturan cosinus berlaku untuk setiap segitiga ABC sebagai berikut:<\/div>\n<div style=\"text-align: center;\"><strong>a<sup>2<\/sup> = b<sup>2<\/sup> + c<sup>2<\/sup> &#8211; 2 bc cos A<\/strong><\/div>\n<div style=\"text-align: center;\"><strong>b<sup>2<\/sup> = c<sup>2<\/sup> + a<sup>2<\/sup> &#8211; 2 ac cos B<\/strong><\/div>\n<div style=\"text-align: center;\"><strong>c<sup>2<\/sup> = a<sup>2<\/sup> + b<sup>2<\/sup> &#8211; 2 ab cos C<\/strong><\/div>\n<div style=\"text-align: justify;\">&nbsp;<\/div>\n<div style=\"text-align: justify;\">Berdasarkan rumus aturan cosinus di atas, maka di dapatkan rumus untuk menghitung besar sudutnya :<\/div>\n<div><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/coss.png\" alt=\"coss.png\" style=\"display: block; margin-left: auto; margin-right: auto; width: 210px;\"><\/div>\n<div>&nbsp;<\/div>\n<div>Supaya kamu lebih paham, kerjakan <strong>contoh soal<\/strong> di bawah ini <em>yuk<\/em> Squad!<\/div>\n<ul style=\"list-style-type: circle;\">\n<li>Segitiga ABC diketahui panjang sisi a = 5 cm, panjang sisi c = 6 cm dan besar sudut B = 60\u00ba. Tentukan panjang sisi b!<\/li>\n<\/ul>\n<p><strong>Diketahui:<\/strong><\/p>\n<p>a = 5 cm<\/p>\n<p>c = 6 cm<\/p>\n<p>B = 60\u00ba<\/p>\n<p style=\"text-align: justify;\"><strong>Ditanya:<\/strong> b?<\/p>\n<p style=\"text-align: justify;\"><strong>Jawab:<\/strong><\/p>\n<p style=\"text-align: justify;\">&nbsp;b<sup>2<\/sup> = a<sup>2<\/sup> + c<sup>2<\/sup> &#8211; 2ac cos B<\/p>\n<p style=\"text-align: justify;\">&nbsp;b<sup>2<\/sup> = 5<sup>2<\/sup> + 6<sup>2<\/sup> &#8211; 2(5)(6) cos 60\u00ba<\/p>\n<p style=\"text-align: justify;\">&nbsp;b<sup>2<\/sup> = 25 + 36 &#8211; 60 (0,5)<\/p>\n<p style=\"text-align: justify;\">&nbsp;b<sup>2<\/sup> = 61 &#8211; 30<\/p>\n<p style=\"text-align: justify;\">&nbsp;b<sup>2<\/sup> = 31<\/p>\n<p style=\"text-align: justify;\">&nbsp;b = 5,56 cm<\/p>\n<p style=\"text-align: justify;\">Jadi, panjang sisi b adalah 5,56 cm<\/p>\n<ul>\n<li style=\"text-align: justify;\"><strong><span style=\"color: #ff0000;\">Baca Juga:<\/span> <a href=\"https:\/\/blog.ruangguru.com\/memahami-fungsi-trigonometri-sederhana\" target=\"_blank\" rel=\"noopener\">Memahami Fungsi Trigonometri Sederhana<\/a><\/strong><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Oke Squad, sekarang kamu sudah paham &#8216;<em>kan<\/em> apa itu aturan sinus dan cosinus? Kalau kamu masih belum puas dengan penjelasan di atas, kamu bisa pelajari lagi melalui<span style=\"background-color: transparent;\"> <\/span><strong style=\"background-color: transparent;\"><a href=\"https:\/\/ruangguru.com\/belajar?utm_medium=referral&amp;utm_source=blog&amp;utm_campaign=apa-itu-aturan-sinus-dan-kosinus\" target=\"_blank\" rel=\"noopener\">ruangbelajar<\/a><\/strong><span style=\"background-color: transparent;\">. Kamu bisa menonton video animasi lengkap dengan soal, pembahasan dan rangkumannya Squad, segera gunakan sekarang.<br \/><\/span><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/link.ruangguru.com\/blPk\/eaff0eb9\" target=\"_blank\" style=\"text-align: center;\" class=\"rg-cta\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/cta\/1f6a4f8b-0326-42d1-bc9c-111ebb100e56.jpeg\" width=\"650\" height=\"228\" alt=\"ruangbelajar\" \/><\/a><\/p>\n<p style=\"text-align: justify;\"><strong>Sumber Referensi:<\/strong><\/p>\n<p style=\"text-align: justify;\"><span>Sinaga, B. Sinambela, P. N J. M. Sitanggang, A. K. dkk. (2017) Matematika. Jakarta: Kemendikbud<\/span><\/p>\n<p style=\"text-align: justify;\">&nbsp;<\/p>\n<p style=\"text-align: justify;\">&nbsp;<\/p>\n<p style=\"text-align: justify;\"><em>Artikel diperbaharui5 Desember 2020<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Squad, kamu pasti sudah tidak asing lagi dengan kata sinus dan cosinus, bukan?&nbsp;Dalam trigonometri, ternyata sinus dan cosinus mempunyai aturan tersendiri, khususnya pada segitiga. Apa itu aturannya? Perbandingan panjang sisi dengan sudut pada segitiga serta menghitung luas segitiga dilakukan dengan menggunakan prinsip trigonometri. Untuk penjelasan selengkapnya, simak di bawah ini ya.<\/p>\n","protected":false},"author":79,"featured_media":10408,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Header%20blog%20RG\/Matematika_10.jpg"],"_edit_last":["1"],"_edit_lock":["1697990157:1"]},"categories":[467,474],"tags":[52,10,256,37],"class_list":["post-10408","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","category-matematika-sma-kelas-10","tag-kelas-10","tag-konsep-pelajaran","tag-matematika-x","tag-sma"],"aioseo_notices":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Apa Itu Aturan Sinus dan Cosinus? | Matematika Kelas 10 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru<\/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:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Apa Itu Aturan Sinus dan Cosinus? | Matematika Kelas 10 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru\" \/>\n<meta property=\"og:description\" content=\"Squad, kamu pasti sudah tidak asing lagi dengan kata sinus dan cosinus, bukan?&nbsp;Dalam trigonometri, ternyata sinus dan cosinus mempunyai aturan tersendiri, khususnya pada segitiga. Apa itu aturannya? Perbandingan panjang sisi dengan sudut pada segitiga serta menghitung luas segitiga dilakukan dengan menggunakan prinsip trigonometri. 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| Matematika Kelas 10 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus","og_locale":"en_US","og_type":"article","og_title":"Apa Itu Aturan Sinus dan Cosinus? | Matematika Kelas 10 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru","og_description":"Squad, kamu pasti sudah tidak asing lagi dengan kata sinus dan cosinus, bukan?&nbsp;Dalam trigonometri, ternyata sinus dan cosinus mempunyai aturan tersendiri, khususnya pada segitiga. Apa itu aturannya? Perbandingan panjang sisi dengan sudut pada segitiga serta menghitung luas segitiga dilakukan dengan menggunakan prinsip trigonometri. Untuk penjelasan selengkapnya, simak di bawah ini ya.","og_url":"https:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus","og_site_name":"Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru","article_publisher":"https:\/\/www.facebook.com\/ruanggurucom\/","article_published_time":"2018-02-28T03:27:24+00:00","article_modified_time":"2023-10-22T15:55:57+00:00","author":"Karina Dwi Adistiana","twitter_card":"summary_large_image","twitter_creator":"@ruangguru","twitter_site":"@ruangguru","twitter_misc":{"Written by":"Karina Dwi Adistiana","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus#article","isPartOf":{"@id":"https:\/\/staging-blog.sirogu.com\/blog\/apa-itu-aturan-sinus-dan-cosinus"},"author":{"name":"Karina Dwi Adistiana","@id":"https:\/\/staging-blog.sirogu.com\/blog\/#\/schema\/person\/cbb994500f3fdab3dc0733faa2e966ea"},"headline":"Apa Itu Aturan Sinus dan Cosinus? 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