{"id":55446,"date":"2019-09-13T16:12:56","date_gmt":"2019-09-13T16:12:56","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=55446"},"modified":"2026-03-25T11:52:26","modified_gmt":"2026-03-25T16:52:26","slug":"law-of-sines","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/law-of-sines\/","title":{"rendered":"Law of Sines"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_BBVXzDZ-9hc\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_BBVXzDZ-9hc\" data-source-videoID=\"BBVXzDZ-9hc\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Law of Sines Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Law of Sines\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_BBVXzDZ-9hc:hover {cursor:pointer;} img#videoThumbnailImage_BBVXzDZ-9hc {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-upper-level-trig-law-of-sines-64c0086bd7f2c-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_BBVXzDZ-9hc\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_BBVXzDZ-9hc\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Law of Sines\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_BBVXzDZ-9hc\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_BBVXzDZ-9hc\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_BBVXzDZ-9hc\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction Lyt_Function() {\n  var x = document.getElementById(\"Lyt\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"Lyt_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"Lyt\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_the_Law_of_Sines\" class=\"smooth-scroll\">What is the Law of Sines?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Finding_the_Missing_Side_of_a_Triangle\" class=\"smooth-scroll\">Finding the Missing Side of a Triangle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Finding_the_Missing_Angle_of_a_Triangle\" class=\"smooth-scroll\">Finding the Missing Angle of a Triangle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Law_of_Sines_Practice_Questions\" class=\"smooth-scroll\">Law of Sines Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label><a href=\"https:\/\/www.mometrix.com\/academy\/law-of-sines-calculator\/\" target=\"none\" style=\"margin: 0 auto;\"><span class=\"accordion_calculator_button\">Calculator<\/span><\/a><\/p>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hi, welcome to this video about the law of sines!<\/p>\n<h2><span id=\"What_is_the_Law_of_Sines\" class=\"m-toc-anchor\"><\/span>What is the Law of Sines?<\/h2>\n<p>\nIf you recall, the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/pythagorean-theorem\/\">Pythagorean theorem<\/a> is useful for finding the missing side of a right triangle.<\/p>\n<p>Our topic today, the law of sines, can be used to help us find the missing side or angle inside any kind of triangle if we have enough information. <\/p>\n<p>Here\u2019s a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">triangle<\/a> we\u2019ll call ABC, with the sides \\(a\\), \\(b\\), and \\(c\\):<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-65143 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/Triangle-ABC.png\" alt=\"Triangle ABC\" width=\"390\" height=\"258\" \/><\/p>\n<p>Notice how \\(\\angle A\\) is opposite side \\(a\\), and how it\u2019s the same for \\(B\\) and \\(C\\). <\/p>\n<p>The law of sines tells us that:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{a}{\\sin{A}}=\\frac{b}{\\sin{B}}=\\frac{c}{\\sin{C}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWhat this means is that the ratios of the length of a side and the sine of its opposite angle are in proportion to the ratio for the other angles and their opposite side. <\/p>\n<h2><span id=\"Finding_the_Missing_Side_of_a_Triangle\" class=\"m-toc-anchor\"><\/span>Finding the Missing Side of a Triangle<\/h2>\n<p>\nLet\u2019s jump right in and use it to find a missing side of a triangle:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-65137 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-two-angles-and-a-side.png\" alt=\"triangle with two angles and a side\" width=\"390\" height=\"258\" \/><\/p>\n<p>The first thing we need to do is check to see if we have enough information to find the missing side. We need one angle and its opposite side length, which we have. We can make one complete ratio using the 35\u00b0 angle and the 10 cm opposite side. Now we just need the angle opposite the missing side, which we have. It\u2019s 70\u00b0. That\u2019s all we need to find the missing side. <\/p>\n<p>It doesn\u2019t matter which side we call \\(a\\) and which side we call \\(b\\). Let\u2019s call our missing side \\(a\\) and its opposite \\(\\angle A\\). And we\u2019ll have that as \\(b\\) and the opposite \\(\\angle B\\). In this case, we don\u2019t need side \\(c\\) or \\(\\angle C\\) at all.<\/p>\n<p>But the law of sines doesn\u2019t have angles in it; instead it has the sine of angles. So we need to use a calculator and find the SIN key. Type in the angle and then hit SIN and you\u2019ll end up with a long decimal for both of our angles:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{a}{0.93969}=\\frac{10\\text{ cm}}{0.57657}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we have a simple proportion to solve. We just need to solve for \\(a\\):<\/p>\n<div class=\"examplesentence\">\\((0.93969)\\) <span style=\"font-size: 120%;\">\\(\\frac{a}{0.93969}=\\frac{10\\text{ cm}}{0.57657}\\)<\/span>\\((0.93969)\\)<br \/>\n\\(a\\approx 16.4\\text{ cm}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe can do a quick mental check that can sometimes catch errors. The larger angle should have a longer side opposite it, and in this case it does (\\(16.4\\text{ cm} >10\\text{ cm}\\)). <\/p>\n<h2><span id=\"Finding_the_Missing_Angle_of_a_Triangle\" class=\"m-toc-anchor\"><\/span>Finding the Missing Angle of a Triangle<\/h2>\n<p>\nBut that\u2019s not all. We can also use the law of sines to find a missing angle in a triangle. Here\u2019s a sample problem:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-65140 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/01\/triangle-with-two-sides-and-an-angle.png\" alt=\"triangle with two sides and an angle\" width=\"390\" height=\"258\" \/><\/p>\n<p>We have two sides and one of their opposite angles, so let\u2019s find the missing opposite angle. When using Law of Sines to find an angle it\u2019s a bit easier if we flip all the ratios, like this:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{\\sin{A}}{a}=\\frac{\\sin{B}}{b}=\\frac{\\sin{C}}{c}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow let\u2019s fill it in. Remember that we only need two of the ratios, and it\u2019s not important which is \\(\\angle A\\) or side <em>a<\/em>, as long as the sine of the angle and its opposite side are together in a ratio. Once again, let\u2019s keep our missing part on the left side and call it <em>A<\/em>. We have:<\/p>\n<div class=\"examplesentence\" style=\"font-size: 120%;\">\\(\\frac{\\sin{A}}{9\\text{ cm}}=\\frac{\\sin{50^{\\circ}}}{8\\text{ cm}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we just solve it by multiplying both sides by 9 cm.<\/p>\n<div class=\"examplesentence\">\\(\\sin{A}=0.86179999\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow all we have to do is find \\(\\angle A\\) instead of \\(\\sin{A}\\). We do this by using the inverse SIN function of your calculator, which is usually written as SIN<sup>r1<\/sup> and can often be accessed by using the 2nd button before hitting SIN. Taking the inverse SIN of 0.8617999 gives us an angle of approximately 59.5 degrees. That\u2019s all there is to it!<\/p>\n<p>Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Law_of_Sines_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Law of Sines Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Law-of-sines-example-1.svg\" alt=\"A triangle with angles labeled 92\u00b0, 54\u00b0, and x. The side opposite the 54\u00b0 angle is labeled 31 cm.\" width=\"288\" height=\"155\" class=\"aligncenter size-full wp-image-274729\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">13.21<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">25.09<\/div><div class=\"PQ\"  id=\"PQ-1-3\">28.75<\/div><div class=\"PQ\"  id=\"PQ-1-4\">31.17<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The law of sines states the following:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin a}{A}=\\dfrac{\\sin b}{B}=\\dfrac{\\sin c}{C}\\)<\/p>\n<p>Filling in the information from this triangle gives:<\/p>\n<p style=\"text-align:center;\">\n\\(\\dfrac{\\sin 92\u00b0}{31}=\\dfrac{\\sin 54\u00b0}{x}\\)<\/p>\n<p>Manipulate to isolate \\(x\\).<\/p>\n<p style=\"text-align:center; line-height: 50px;\">\n\\(x\\sin 92\u00b0=31\\sin 54\u00b0\\)<br \/>\n\\(x=\\dfrac{31\\sin 54\u00b0}{\\sin 92\u00b0}\\)<br \/>\n\\(x \\approx 25.09\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Law-of-sines-example-2.svg\" alt=\"A triangle with angles of 23\u00b0 and 117\u00b0, one side labeled 11 cm, and another side labeled x.\" width=\"275\" height=\"184\" class=\"aligncenter size-full wp-image-274732\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">25.08<\/div><div class=\"PQ\"  id=\"PQ-2-2\">13.14<\/div><div class=\"PQ\"  id=\"PQ-2-3\">29.17<\/div><div class=\"PQ\"  id=\"PQ-2-4\">18.52<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The law of sines states the following:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin a}{A}=\\dfrac{\\sin b}{B}=\\dfrac{\\sin c}{C}\\)<\/p>\n<p>Filling in the information from this triangle gives:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin 23\u00b0}{11}=\\dfrac{\\sin 117\u00b0}{x}\\)<\/p>\n<p>Manipulate to solve for \\(x\\).<\/p>\n<p style=\"text-align:center; line-height: 50px;\">\n\\(x\\sin 23\u00b0=11\\sin 117\u00b0\\)<br \/>\n\\(x=\\dfrac{11\\sin 117\u00b0}{\\sin 23\u00b0}\\)<br \/>\n\\(x \\approx 25.08\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Law-of-sines-example-3.svg\" alt=\"A triangle with angles 25\u00b0 and x\u00b0, and sides 21 cm and 13 cm shown.\" width=\"359\" height=\"161\" class=\"aligncenter size-full wp-image-274735\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">83.92\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-2\">82.13\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-3\">49.17\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">43.05\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The law of sines states the following:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin a}{A}=\\dfrac{\\sin b}{B}=\\dfrac{\\sin c}{C}\\)<\/p>\n<p>Filling in the information from this triangle gives:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin 25\u00b0}{13}=\\dfrac{\\sin x}{21}\\)<\/p>\n<p>Manipulate to solve for \\(x\\).<\/p>\n<p style=\"text-align: center; margin-bottom: 1em\">\\(21\\sin 25\u00b0=13\\sin x\\)<\/p>\n<p style=\"text-align: center; margin-bottom: 1.5em\">\\(\\dfrac{21\\sin 25\u00b0}{13}=\\sin x\\)<\/p>\n<p style=\"text-align: center; margin-bottom: 1em\">\\(\\sin^{-1}(\\dfrac{21\\sin 25\u00b0}{13})=x\\)<\/p>\n<p style=\"text-align: center;\">\\(x \\approx 43.05\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Law-of-sines-example-4.svg\" alt=\"Triangle with sides of 31 cm and 24 cm, an angle of 37\u00b0 between them, and an unknown angle labeled x\u00b0.\" width=\"277\" height=\"137\" class=\"aligncenter size-full wp-image-274738\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">58.91\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-2\">39.84\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-3\">47.17\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">51.02\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The law of sines states the following:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin a}{A}=\\dfrac{\\sin b}{B}=\\dfrac{\\sin c}{C}\\)<\/p>\n<p>Filling in the information from this triangle gives:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin 37\u00b0}{24}=\\dfrac{\\sin x}{31}\\)<\/p>\n<p>Manipulate to solve for \\(x\\).<\/p>\n<p style=\"text-align: center; margin-bottom: 1em\">\\(31\\sin 37\u00b0=24\\sin x\\)<\/p>\n<p style=\"text-align: center; margin-bottom: 1.5em\">\\(\\dfrac{31\\sin 37\u00b0}{24}=\\sin x\\)<\/p>\n<p style=\"text-align: center; margin-bottom: 1em\">\\(\\sin^{-1}(\\dfrac{31\\sin 37\u00b0}{24})=x\\)<\/p>\n<p style=\"text-align: center;\">\\(x \\approx 51.02\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Law-of-sines-example-5.svg\" alt=\"A triangle with angles 27\u00b0 and 137\u00b0, a side measuring 42 cm, and an unknown side labeled x.\" width=\"359\" height=\"181\" class=\"aligncenter size-full wp-image-274726\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">29.86<\/div><div class=\"PQ\"  id=\"PQ-5-2\">31.48<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">27.96<\/div><div class=\"PQ\"  id=\"PQ-5-4\">22.47<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The law of sines states the following:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin a}{A}=\\dfrac{\\sin b}{B}=\\dfrac{\\sin c}{C}\\)<\/p>\n<p>Filling in the information from this triangle gives:<\/p>\n<p style=\"text-align:center;\">\\(\\dfrac{\\sin 137\u00b0}{42}=\\dfrac{\\sin 27\u00b0}{x}\\)<\/p>\n<p>Manipulate to isolate \\(x\\).<\/p>\n<p style=\"text-align:center; line-height: 50px;\">\n\\(x\\sin 137\u00b0=42\\sin 27\u00b0\\)<br \/>\n\\(x=\\dfrac{42\\sin 27\u00b0}{\\sin 137\u00b0}\\)<br \/>\n\\(x \\approx 27.96\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/trigonometry\/\">Return to Trigonometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Trigonometry Videos<\/p>\n","protected":false},"author":1,"featured_media":186674,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-55446","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-sine-videos","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/55446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=55446"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/55446\/revisions"}],"predecessor-version":[{"id":279295,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/55446\/revisions\/279295"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/186674"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=55446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}