{"id":59243,"date":"2020-06-02T13:30:07","date_gmt":"2020-06-02T13:30:07","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=59243"},"modified":"2026-03-28T10:35:25","modified_gmt":"2026-03-28T15:35:25","slug":"sine","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/sine\/","title":{"rendered":"Sine"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_Twz3rmpnnYc\" 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_Twz3rmpnnYc\" data-source-videoID=\"Twz3rmpnnYc\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Sine Video\" height=\"1080\" width=\"1920\" class=\"size-full\" data-matomo-title = \"Sine\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_Twz3rmpnnYc:hover {cursor:pointer;} img#videoThumbnailImage_Twz3rmpnnYc {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/01\/Sine-thumb.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_Twz3rmpnnYc\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_Twz3rmpnnYc\" 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\",\"Sine\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Twz3rmpnnYc\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Twz3rmpnnYc\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_Twz3rmpnnYc\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction ajI_Function() {\n  var x = document.getElementById(\"ajI\");\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=\"ajI_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=\"ajI\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Solving_Right_Triangles\" class=\"smooth-scroll\">Solving Right Triangles<\/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=\"#Graphing_Using_Sine\" class=\"smooth-scroll\">Graphing Using Sine<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Using_Trig_Identities\" class=\"smooth-scroll\">Using Trig Identities<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Sine_Practice_Questions\" class=\"smooth-scroll\">Sine 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, and welcome to this review of sine! Today we\u2019re going to dig into what sine functions are all about and take a look at three types of problems where you\u2019ll \ufb01nd them. <\/p>\n<h2><span id=\"Solving_Right_Triangles\" class=\"m-toc-anchor\"><\/span>Solving Right Triangles<\/h2>\n<p>\nFirst, let\u2019s look at the main use of trigonometric functions, which is to solve <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">right triangles<\/a>.<\/p>\n<p>Here\u2019s an example:<\/p>\n<p>Our goal is to \ufb01nd the measure of angle \\(x\\). We know all the side lengths, and know there is a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/angles\/\">right angle<\/a> which measures 90 degrees. But the other two angles are unknown.<\/p>\n<p>Because the sum of the interior angles of a triangle must add up to 180 degrees, we know that angle \\(x\\) and the other unknown angle must add up to 90 but we have no idea how they do so. They could both be 45 degrees or one could be 50 and the other 40 or 30 and 60 and so on.<\/p>\n<p>There\u2019s no way for us to know, unless we use a bit of trigonometry, specifically sine.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/03\/59243-01.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>Sine, which is commonly abbreviated to S-I-N, is the ratio of the side opposite the angle we want to know over the hypotenuse of the right triangle. <\/p>\n<div class=\"examplesentence\" style=\"font-size: 110%;\"><strong>Sine Formula<\/strong><br \/>\n\\(\\text{sin }\u03b8=\\frac{\\text{opposite}}{\\text{hypotenuse}}=\\frac{\\text{o}}{\\text{h}}\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember that the hypotenuse is the longest side and is always opposite the right angle, which is the largest angle in any right triangle.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/03\/59243-02.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>When dealing with trigonometric ratios, it\u2019s common to use SOH-CAH-TOA to help you remember them. The \ufb01rst part of it, SOH, helps us remember that Sine is the Opposite over<br \/>\nthe Hypotenuse.<\/p>\n<p>Because the hypotenuse will always be longer than the opposite side, this means the possible values for sine when used in a triangle like this are between 0 and 1. In our sample triangle, the side opposite angle \\(x\\) has a length of 12 and the hypotenuse has a length of 20.<\/p>\n<div class=\"examplesentence\">\\(sin x = \\frac{12}{20} = 0.6\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we know that the sine of x is equal to 0.6 when we convert the fraction to a decimal by dividing the numerator by the denominator.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/03\/59243-03.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>Now we need to use a calculator to \ufb01nd our angle. In the old days before calculators this had to be done by looking through pages and pages of SIN tables to \ufb01nd the value of SIN x that corresponded to the measure of angle x. That still works, but it\u2019s easier on a calculator.<\/p>\n<p>First, find the SIN button on your calculator. This button is usually used when you know the angle and you want to \ufb01nd the ratio of the opposite side to the hypotenuse. We want to do the opposite, and \ufb01nd the angle from the ratio that we have already calculated (0.6). So what we need is the ARC SIN, which is often labeled as ASIN or, even more commonly, as SIN-1. Note that the -1 exponent here does not represent the reciprocal, but the inverse operation of SIN. This is accessed by hitting the 2nd key and then the SIN key.<\/p>\n<p>Okay, so we type in 0.6 and then 2nd and then SIN and our calculator displays 36.86989765,or approximately 36.87 degrees. We\u2019ve done it!<\/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>\nWe can also use sine to \ufb01nd a missing side if we happen to know an angle of the triangle and the hypotenuse. Here\u2019s another sample problem:<\/p>\n<p>Okay, let&#8217;s set up our equation. We know the angle is 30 degrees, so the left side of our equation is the sine of 30 degrees. This is set equal to the opposite side, which is \\(x\\), over the<br \/>\nhypotenuse, which is 14.<\/p>\n<div class=\"examplesentence\">\\(sin 30\u00b0 = \\frac{x}{14}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe sine of 30 degrees is a number that we can \ufb01nd by using our calculator. We just type in 30 and hit the SIN key and we get a value of 0.5. So now our equation looks like this:<\/p>\n<div class=\"examplesentence\">\\(0.5 = \\frac{x}{14}\\)<\/div>\n<p>\n&nbsp;<br \/>\nTo solve, we multiply both sides by 14 and we \ufb01nd that \\(x\\) has a value of 7. Success!<\/p>\n<p>Okay, so far we have used sine to \ufb01nd a missing angle and a missing side in a right triangle. What else is it used for?<\/p>\n<h2><span id=\"Graphing_Using_Sine\" class=\"m-toc-anchor\"><\/span>Graphing Using Sine<\/h2>\n<p>\nOur second use of sine is for graphing. Let\u2019s set up the simplest sine function:<\/p>\n<p>This is a sine wave. It\u2019s maximum \\(y\\)-value is 1 and it\u2019s minimum y-value is -1. That\u2019s a bit di\ufb00erent than in our triangle, where we couldn\u2019t have a negative value of the sine function, but that was because our opposite and hypotenuse sides were always positive.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/03\/sine-1-scaled.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<p>Let\u2019s look closely at the \\(x\\)-values.<\/p>\n<p>Notice that these are not angle measures, since there is no degree symbol on the numbers. Instead, we\u2019re using radians. You may have noticed that on your calculator you can choose between degrees and radians. Converting between radians and degrees requires you to know that pi radians = 180 degrees.<\/p>\n<p>Look at our graph. Since pi is approximately 3.14 we can look just to the right of the 3 on our \\(x\\)-axis and see that the graph touches the \\(x\\)-axis right where \\(\\pi\\) is located. We can test this by making sure our calculator is in Radian mode (RAD), hitting the pi key and then the SIN key. We get a value of 0, which shows we interpreted that correctly.<\/p>\n<p>Let\u2019s try it again but this time in Degree mode (DEG). Let\u2019s use the equivalent of pi which is 180 degrees. Make sure your calculator is in Degree mode, type in 180 and hit the SIN key. Again we get 0!<\/p>\n<p>The peak of the wave is halfway between 0 and pi, so if we are in radian mode, hit the pi key and divide by two and then hit the SIN key we\u2019ll get a value of 1.<\/p>\n<h2><span id=\"Using_Trig_Identities\" class=\"m-toc-anchor\"><\/span>Using Trig Identities<\/h2>\n<p>\nThe third place we\u2019ll see sine is when using trigonometric identities. There are a lot of trig identities, and they are used to simplify expressions or equations. It\u2019s kind of like a puzzle where you need to \ufb01nd the right identity so that you can substitute and simplify by cancelling.<\/p>\n<p>Let\u2019s take a look at a relatively easy one:<\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{\\text{sin }x \\times \\text{csc }x}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe haven\u2019t seen cosecant of \\(x\\) yet, but if we look it up we \ufb01nd that it is equal to the hypotenuse over the opposite, or, more usefully, the reciprocal of the sine!<\/p>\n<div class=\"examplesentence\">\\(csc x = \\frac{h}{o}\\) or \\(\\frac{1}{\\text{sin }x}\\)<\/div>\n<p>\n&nbsp;<br \/>\nGoing back to our problem, we can substitute one over the sine of \\(x\\) for cosecant of \\(x\\), which give us this:<\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{\\text{sin }x} \\times \\frac{1}{\\text{scs }x}=\\frac{1}{\\text{sin }x} \\times \\frac{1}{\\frac{1}{\\text{sin }x}}=\\frac{1}{\\text{sin }x}\\times \\frac{\\text{sin }x}{1}=\\frac{\\text{sin }x}{\\text{sin }x}=1\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd that\u2019s all there is to it! As you can see, sine comes in handy when graphing, solving problems with angles, and determining trigonometric identities.<\/p>\n<p>I hope this review was helpful! Thanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/sine.html\"target=\"_blank\">\u201cThe Sine Function &#8211; Math Word Definition &#8211; Math Open Reference.\u201d <\/a><\/li>\n<li><a href=\"https:\/\/www.mathopenref.com\/trigfunctions.html\"target=\"_blank\">\u201cIntroduction to the 6 Trigonometry Functions &#8211; Math Open Reference.\u201d <\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Sine_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Sine 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 the measure of \\(\\angle X\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/11\/Sine-triangle-example-1.svg\" alt=\"A right triangle XYZ with sides XY = 4 cm, YZ = 3 cm, and right angle at Z. The base XZ is labeled as y.\" width=\"211\" height=\"208\" class=\"aligncenter size-full wp-image-275125\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">55.6\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-2\">49.2\u00b0<\/div><div class=\"PQ\"  id=\"PQ-1-3\">53.6\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">48.59\u00b0<\/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 opposite and hypotenuse side lengths are provided with the right triangle. This means that we can solve for \\(\\angle X\\) by using a sine trig function.<\/p>\n<p>The equation will start out as \\(\\sin x=\\frac{3}{4}\\). In order to solve for \\(x\\), we need to use the inverse of the function, so the equation \\(\\sin x=\\frac{3}{4}\\) becomes \\(x=\\sin^{-1}(\\frac{3}{4})\\), which simplifies to approximately 48.59\u00b0.<\/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 the hypotenuse AB in the following right triangle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/11\/Sine-triangle-example-2.svg\" alt=\"A triangle labeled ABC with angle B at 62 degrees, angle C as a right angle, and side AC measuring 25 feet.\" width=\"285\" height=\"155\" class=\"aligncenter size-full wp-image-275128\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">21.32<\/div><div class=\"PQ\"  id=\"PQ-2-2\">43.32<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">28.31<\/div><div class=\"PQ\"  id=\"PQ-2-4\">35.21<\/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 sine trig function can be used to solve for the hypotenuse of this triangle by setting up the following equation:<\/p>\n<p style=\"text-align: center\">\\(\\sin 62=\\dfrac{25}{x}\\)<\/p>\n<p>We can determine that \\(\\sin 62\\) is equivalent to 0.883, so the equation becomes \\(0.883=\\frac{25}{x}\\), which simplifies to approximately 28.31.<\/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 \/>\nWhat needs to be provided in order to solve for an unknown angle using the sine trig function?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Adjacent and hypotenuse <\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">Opposite and hypotenuse <\/div><div class=\"PQ\"  id=\"PQ-3-3\">Opposite and adjacent <\/div><div class=\"PQ\"  id=\"PQ-3-4\">Hypotenuse and obtuse <\/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>SOH-CAH-TOA is a helpful mnemonic device to remember the three basic trig ratios (sine, cosine, and tangent). SOH refers to the following:<\/p>\n<p style=\"text-align: center\">\\(\\text{sine}=\\dfrac{\\text{opposite}}{\\text{hypotenuse}}\\)<\/p>\n<p>When using the sine trig ratio, the opposite and hypotenuse need to be provided in order to solve for a missing angle measure.<\/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 \/>\nSuppose you want to build a ramp that reaches a doorway that is four feet above the ground. How long will the ramp need to be if you want the angle of elevation to be 20\u00b0?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/11\/Sine-triangle-example-3.svg\" alt=\"Right triangle with a 20-degree angle, a vertical side labeled 4 ft, and the hypotenuse labeled with a question mark.\" width=\"288\" height=\"96\" class=\"aligncenter size-full wp-image-275119\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">11.7 feet<\/div><div class=\"PQ\"  id=\"PQ-4-2\">21.7 feet<\/div><div class=\"PQ\"  id=\"PQ-4-3\">13.5 feet<\/div><div class=\"PQ\"  id=\"PQ-4-4\">17.5 feet<\/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 sine trig function can be used to solve for the length of the hypotenuse using the equation \\(\\sin 20=\\frac{4}{x}\\).<\/p>\n<p>We can determine that \\(\\sin 20\\) is equivalent to 0.3420, so the equation becomes \\(0.3420=\\frac{4}{x}\\). This simplifies to approximately 11.7 feet.<\/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 \/>\nHow high off the ground is Thomas\u2019s kite if the string from the kite is extended to 50 meters, and the angle of elevation created from the ground and the kite is 12\u00b0? <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/11\/Sine-triangle-example-4.svg\" alt=\"A person holds a kite string at a 12-degree angle above the ground; the string measures 50 meters in length.\" width=\"441\" height=\"217\" class=\"aligncenter size-full wp-image-275122\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(x=14.4 \\text{ ft}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(x=12.4 \\text{ ft}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(x=10.4 \\text{ ft}\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(x=8.4 \\text{ ft}\\)<\/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 height of the kite can be determined by setting up a trig function. The sine trig function will be used, and the equation will start as:<\/p>\n<p style=\"text-align: center\">\\(\\sin 12=\\dfrac{x}{50}\\)<\/p>\n<p>We can determine that \\(\\sin 12\\) simplifies to 0.2079, so the equation becomes \\(\\approx 0.2079=\\frac{x}{50}\\). When both sides of the equation are multiplied by 50, the value of \\(x\\) is about 10.4.<\/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":211879,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-59243","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\/59243","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=59243"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/59243\/revisions"}],"predecessor-version":[{"id":261238,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/59243\/revisions\/261238"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/211879"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=59243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}