{"id":13125,"date":"2014-02-07T17:00:14","date_gmt":"2014-02-07T17:00:14","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=13125"},"modified":"2026-03-26T10:10:53","modified_gmt":"2026-03-26T15:10:53","slug":"inverse-of-cosine","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/inverse-of-cosine\/","title":{"rendered":"Inverse Trig Functions"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_YD8OlA89URs\" 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_YD8OlA89URs\" data-source-videoID=\"YD8OlA89URs\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Inverse Trig Functions Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Inverse Trig Functions\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_YD8OlA89URs:hover {cursor:pointer;} img#videoThumbnailImage_YD8OlA89URs {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1316-inverse-functions-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_YD8OlA89URs\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_YD8OlA89URs\" 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\",\"Inverse Trig Functions\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_YD8OlA89URs\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_YD8OlA89URs\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_YD8OlA89URs\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction JsP_Function() {\n  var x = document.getElementById(\"JsP\");\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=\"JsP_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=\"JsP\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Normal_Trig_Functions\" class=\"smooth-scroll\">Normal Trig Functions<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#SOHCAHTOA\" class=\"smooth-scroll\">SOHCAHTOA<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Inverse_Trig_Functions_Practice_Questions\" class=\"smooth-scroll\">Inverse Trig Functions 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>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on inverse trig functions!<\/p>\n<h2><span id=\"Normal_Trig_Functions\" class=\"m-toc-anchor\"><\/span>Normal Trig Functions<\/h2>\n<p>\nIn order to understand what inverse trig functions are, let\u2019s first review what normal trigonometric functions are.<\/p>\n<p>Remember, the common three trig functions are <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/sine\/\">sine<\/a>, <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/cosine\/\">cosine<\/a>, and <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/finding-tangent\/\">tangent<\/a>. These trig functions are used to relate a triangle\u2019s side and angle measures to one another.<\/p>\n<p>For instance, we would use tangent in a problem where we need to find the missing side length of a triangle.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-71800\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1.png\" alt=\"right triangle, bottom left angle 30 degrees, bottom right angle marked with a square, bottom side labeled &quot;x&quot;, right side labeled 3, words on the right say &quot;Trig Functions sin cos tan&quot;, bottom words say &quot;SOH-CAH-TOA&quot;\" width=\"777\" height=\"437\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-1-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<h2><span id=\"SOHCAHTOA\" class=\"m-toc-anchor\"><\/span>SOHCAHTOA<\/h2>\n<p>\nIf we remember SOH-CAH-TOA, we can see that this triangle uses TOA, which stands for \\(\\tan{\\theta} =\\frac{opposite}{adjacent} \\).<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nIf we plug in the values for our triangle, we get \\(\\tan {30} =\\frac{3}{x}\\).<\/p>\n<p>Rearranging to get \\(x\\) by itself gives us \\(x=\\frac{3}{tan 30}\\).<\/p>\n<p>This then simplifies to \\(x\\approx 5.20\\).<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nBut what if we are given a triangle where we know the side measures but we want to know the angle measure, like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-71803\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2.png\" alt=\"right triangle, left side 7, bottom side 18, bottom left angle marked with a square, bottom right angle marked x degrees\" width=\"777\" height=\"437\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-2-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p>If we plug it into our TOA equation, we get \\(tan x =\\frac{7}{18}\\).<\/p>\n<p>We want to get the \\(x\\)-value by itself, so we need to \u201cundo\u201d the tangent somehow. This is where inverse trig functions come in handy. Inverse trig functions are just the opposite of trig functions.<\/p>\n<p>The inverse of tangent is written as: \\(\\arctan{x}\\) (which can look like \\(\\text{atan }x\\)) or \\(\\tan^{-1}{x}\\) (or tan inverse \\(x\\)). Sine and cosine work the same way; just replace \u201ctangent\u201d with either \u201csine\u201d or \u201ccosine.\u201d<\/p>\n<p>If we apply this to our example, we get \\(x=\\arctan \\frac{7}{18}\\).<\/p>\n<p>Now, all we have to do is plug this into our calculator and then we have our answer! The inverse trig functions are typically found by hitting the 2nd key and then the trig function key. If we do this, we find that \\(x\\approx 21.25^{\\circ}\\).<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nLet\u2019s try another example. Use inverse trig functions to solve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-71806\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3.png\" alt=\"right triangle, right side hypotenuse 6, bottom side 3, top left angle marked x degrees, bottom left angle marked with a square\" width=\"777\" height=\"437\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-3-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/> <\/p>\n<p>We are looking for our angle and we are given the opposite and hypotenuse side measures, so we are going to use SOH: \\(\\sin {x} =\\frac{3}{6}\\).<\/p>\n<p>If we isolate \\(x\\) by itself, we get \\(x=\\sin^{-1}{\\frac{3}{6}}\\).<\/p>\n<p>Remember, \\(\\text{asin }x\\) and \\(\\sin^{-1}{x}\\) mean the same thing, so the notation can be used interchangeably. <\/p>\n<p>When we plug this into our calculator, we see that \\(x=30^{\\circ}\\).<\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nI want you to try one more, but this time do it on your own. After I show you the problem, pause the video and work it out. Then when you finish, see if your answer matches up with mine.<\/p>\n<p>Solve for \\(x\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-71809\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4.png\" alt=\"right triangle, left side hypotenuse 22, right side 9, top right angle x degrees, bottom right angle marked with a square\" width=\"777\" height=\"437\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/Inverse-Trig-Functions-4-1536x864.png 1536w\" sizes=\"auto, (max-width: 777px) 100vw, 777px\" \/><\/p>\n<p>In this problem, we are given our adjacent and hypotenuse sides and we are looking for the angle between them. This means we are going to use CAH. If we set up our equation, it will look like this: \\(\\cos {x} =\\frac{9}{22}\\).<\/p>\n<p>Solving for \\(x\\) by itself gives us \\(x=\\cos^{-1}\\frac{9}{22}\\).<\/p>\n<p>When we plug this into our calculator, we get \\(x\\approx 65.85^{\\circ}\\).<\/p>\n<hr>\n<p>\nRemember, inverse trig functions are just the opposite of trig functions. Trig functions are used to find the ratio of the sides of a triangle as related to the angle, and inverse trig functions help you figure out what that angle measure is when given the ratio of the sides. <\/p>\n<p>I hope this review on inverse trig functions was helpful. Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Inverse_Trig_Functions_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Inverse Trig Functions 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 \/>\nWhich of the following shows an incorrect way to express the inverse of a tangent trig function?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(\\arctan x\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(\\text{atan } x\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\(\\tan^{-1}x\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">\\(\\text{atan}^{-1\\:}x\\)<\/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 inverse of a tangent trig function can be written as \\(\\arctan x\\), \\(\\text{atan }x\\), or \\(\\tan^{-1}x\\). Inverse trig functions are used to calculate the angle measures of a right triangle, when the side measures are known. <\/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 \/>\nWhat is the measure of \\(\\angle x\\)?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-97738\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-11-and-8.png\" alt=\"Right triangle with side lengths 11 and 8\" width=\"230.4\" height=\"228.6\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-11-and-8.png 744w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-11-and-8-300x298.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-11-and-8-150x150.png 150w\" sizes=\"(max-width: 744px) 100vw, 744px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">53.7\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">46.7\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-3\">36.7\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-4\">40.7\u00b0<\/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>We know that the opposite side is 8 and the hypotenuse is 11. This means that SOH will be used, or the sine function.<\/p>\n<p>The sine function refers to \u201copposite over hypotenuse,\u201d so when the equation is set up, it will show 8 over 11. The equation starts as:<\/p>\n<p style=\"text-align: center\">\\(\\sin x=\\dfrac{8}{11}\\)<\/p>\n<p>In order to solve for \\(x\\), we need to use the inverse of this trig function:<\/p>\n<p style=\"text-align: center\">\\(x=\\sin^{-1}\\dfrac{8}{11}\\)<\/p>\n<p>This simplifies to approximately 46.7\u00b0.<\/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 \/>\nWill the following angle be found using sine, cosine, or tangent?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-97741\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-12-and-9.png\" alt=\"Right triangle with side lengths 12 and 9\" width=\"313\" height=\"205\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-12-and-9.png 1008w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-12-and-9-300x197.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Right-triangle-with-side-lengths-12-and-9-768x504.png 768w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">Sine<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">Cosine<\/div><div class=\"PQ\"  id=\"PQ-3-3\">Tangent<\/div><div class=\"PQ\"  id=\"PQ-3-4\">Inverse<\/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 unknown angle will be identified using the cosine trig function. The adjacent side length and the hypotenuse are provided, which means CAH, or cosine will be used.<\/p>\n<p>The angle would be identified using the equation \\(x=\\cos^{-1}\\frac{9}{12}\\), which simplifies to 41.4\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 \/>\nA tree that is 51 feet tall casts a shadow that is 62 feet long. What is the angle of elevation formed between the ground and the blue line?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-97744\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Tree-length-of-51ft-casting-a-shadow-that-is-62ft.png\" alt=\"Tree length of 51ft casting a shadow that is 62ft\" width=\"468\" height=\"255\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Tree-length-of-51ft-casting-a-shadow-that-is-62ft.png 1483w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Tree-length-of-51ft-casting-a-shadow-that-is-62ft-300x164.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Tree-length-of-51ft-casting-a-shadow-that-is-62ft-1024x559.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/Tree-length-of-51ft-casting-a-shadow-that-is-62ft-768x419.png 768w\" sizes=\"auto, (max-width: 468px) 100vw, 468px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">29.4\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-2\">51.4\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">39.4\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-4\">44.4\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 opposite and adjacent side lengths are provided, so the TOA, or tangent function will be used.<\/p>\n<p>The equation will start out as:<\/p>\n<p style=\"text-align: center\">\\(\\tan x=\\dfrac{51}{62}\\)<\/p>\n<p>In order to solve for \\(x\\) we will need to use the inverse of this trig function.<\/p>\n<p style=\"text-align: center\">\\(x=\\tan^{-1}\\dfrac{51}{62}\\)<\/p>\n<p>Thus simplifies to \\(x=39.4\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 \/>\nWhat is the angle created by the ladder and ground in order for the ladder to reach the top of a ten-foot wall that is three feet from the base of the ladder?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-97735\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/10ft-wall-that-has-a-ladder-laying-across-it-that-is-3ft-away.png\" alt=\"10ft wall that has a ladder laying across it that is 3ft away\" width=\"288.9\" height=\"350.1\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/10ft-wall-that-has-a-ladder-laying-across-it-that-is-3ft-away.png 719w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/10\/10ft-wall-that-has-a-ladder-laying-across-it-that-is-3ft-away-248x300.png 248w\" sizes=\"(max-width: 719px) 100vw, 719px\" \/> <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">73.3\u00b0<\/div><div class=\"PQ\"  id=\"PQ-5-2\">63.3\u00b0<\/div><div class=\"PQ\"  id=\"PQ-5-3\">81.3\u00b0<\/div><div class=\"PQ\"  id=\"PQ-5-4\">79.3\u00b0<\/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>\\(\\angle x\\) can be calculated using an inverse trig function. The side lengths that are opposite and adjacent to \\(\\angle x\\) are provided, which represents TOA, or the tangent function.<\/p>\n<p>The equation will start out as:<\/p>\n<p style=\"text-align: center\">\\(\\tan x=\\dfrac{10}{3}\\)<\/p>\n<p>In order to solve for \\(x\\) we need to use the inverse of this trig function.<\/p>\n<p style=\"text-align: center\">\\(x=\\tan^{-1}\\dfrac{10}{3}\\)<\/p>\n<p>This simplifies to \\(x=73.3\\), which means that the measure of \\(\\angle x\\) is \\(73.3\u00b0\\).<\/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":100393,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-13125","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-cosine-videos","7":"page_category-math-advertising-group","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\/13125","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=13125"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/13125\/revisions"}],"predecessor-version":[{"id":280202,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/13125\/revisions\/280202"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100393"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=13125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}