{"id":154502,"date":"2022-03-25T23:36:22","date_gmt":"2022-03-25T18:06:22","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/law-of-sines-explanation-proof-formula-and-solved-examples\/"},"modified":"2022-12-31T16:06:54","modified_gmt":"2022-12-31T10:36:54","slug":"law-of-sines-explanation-proof-formula-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/law-of-sines\/","title":{"rendered":"Law of Sines \u2013 Explanation, Proof, Formula and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/law-of-sines\/#Introduction_to_the_Law_of_Sines\" title=\"Introduction to the Law of Sines\">Introduction to the Law of Sines<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/law-of-sines\/#Define_Law_of_Sines\" title=\"Define Law of Sines\">Define Law of Sines<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/law-of-sines\/#Sine_Rule_Proof\" title=\"Sine Rule Proof\">Sine Rule Proof<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/law-of-sines\/#The_Formula_For_Sine_Rule\" title=\"The Formula For Sine Rule\">The Formula For Sine Rule<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_the_Law_of_Sines\"><\/span>Introduction to the Law of Sines<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The law of sines is a mathematical statement that relates the angles of a triangle to the lengths of its sides. The law states that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. This relationship can be used to solve for any angle or side in a triangle.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154501 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/law-of-sines-explanation-proof-formula-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/law-of-sines-explanation-proof-formula-and-solved-examples.jpg?v=1648231579 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/law-of-sines-explanation-proof-formula-and-solved-examples-300x212.jpg?v=1648231579 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Define_Law_of_Sines\"><\/span>Define Law of Sines<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The law of sines states that the ratio of the length of the opposite side to the length of the hypotenuse is the same for all three sides of a triangle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Sine_Rule_Proof\"><\/span>Sine Rule Proof<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sine rule states that the sine of an angle is equal to the sine of its adjacent angle multiplied by the cosine of the angle between them.<\/p>\n<p>Proof:<\/p>\n<p>Let A be an angle and let B be its adjacent angle. Let C be the angle between A and B.<\/p>\n<p>We will show that:<\/p>\n<p>sin A = sin B \u00d7 cos C<\/p>\n<p>We can use the Pythagorean theorem to show that:<\/p>\n<p>cos C = (length of BC)\u00b2 &#8211; (length of AC)\u00b2<\/p>\n<p>Now, we can substitute this into the equation to get:<\/p>\n<p>sin A = sin B \u00d7 (length of BC)\u00b2\/(length of AC)\u00b2<\/p>\n<p>sin A = sin B \u00d7 (cos C)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Formula_For_Sine_Rule\"><\/span>The Formula For Sine Rule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sine rule states that the sine of an angle is equal to the sine of its opposite side divided by the length of the opposite side.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introduction to the Law of Sines The law of sines is a mathematical statement that relates the angles of a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Law of Sines","_yoast_wpseo_title":"Law of Sines \u2013 Explanation, Proof, Formula and Solved Examples?","_yoast_wpseo_metadesc":"Learn about law of sines topic of maths in details explained by subject experts on infinitylearn.com. 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