{"id":280967,"date":"2025-08-05T09:45:49","date_gmt":"2025-08-05T09:45:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=280967"},"modified":"2025-08-05T09:45:52","modified_gmt":"2025-08-05T09:45:52","slug":"a-20-foot-ladder-is-set-up-against-a-building-so-that-the-ladder-makes-an-angle-of-73-with-the-ground","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/08\/05\/a-20-foot-ladder-is-set-up-against-a-building-so-that-the-ladder-makes-an-angle-of-73-with-the-ground\/","title":{"rendered":"A 20-foot ladder is set up against a building so that the ladder makes an angle of 73\u00b0 with the ground."},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/image-513.png\" alt=\"\" class=\"wp-image-280968\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is&nbsp;<strong>19.1 ft<\/strong>.<\/p>\n\n\n\n<p>This problem can be solved using trigonometry by recognizing that the ladder, the building, and the ground form a right-angled triangle. The goal is to find the height&nbsp;h, which is the side opposite the given angle.<\/p>\n\n\n\n<p>First, we must identify the components of the right triangle in relation to the 73-degree angle. The 20-foot ladder is the longest side of the triangle, positioned opposite the right angle, which makes it the&nbsp;<strong>hypotenuse<\/strong>. The height&nbsp;h&nbsp;is the side directly across from the 73-degree angle, making it the&nbsp;<strong>opposite<\/strong>&nbsp;side. The distance&nbsp;b&nbsp;along the ground is the side next to the 73-degree angle, making it the&nbsp;<strong>adjacent<\/strong>&nbsp;side.<\/p>\n\n\n\n<p>To find the height&nbsp;h, we need a trigonometric function that relates the side we want to find (opposite) with the side we know (hypotenuse). The mnemonic SOH CAH TOA helps us choose the correct function. SOH stands for Sine equals Opposite over Hypotenuse. This is the perfect choice for our problem.<\/p>\n\n\n\n<p>The formula is:<br>sin(angle) = Opposite \/ Hypotenuse<\/p>\n\n\n\n<p>Plugging in the known values from the problem:<br>sin(73\u00b0) = h \/ 20<\/p>\n\n\n\n<p>From the provided table of values, we know that sin(73\u00b0) is approximately 0.9563. We can substitute this value into our equation:<br>0.9563 = h \/ 20<\/p>\n\n\n\n<p>To solve for&nbsp;h, we need to isolate it. We can do this by multiplying both sides of the equation by 20:<br>h = 20 * 0.9563<\/p>\n\n\n\n<p>Performing the multiplication gives us:<br>h \u2248 19.126 feet<\/p>\n\n\n\n<p>When we compare this result to the available options, the value 19.126 ft is closest to 19.1 ft. Therefore, the approximate height of the ladder on the building is 19.1 feet.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/08\/learnexams-banner5-317.jpeg\" alt=\"\" class=\"wp-image-280969\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The correct answer is&nbsp;19.1 ft. This problem can be solved using trigonometry by recognizing that the ladder, the building, and the ground form a right-angled triangle. The goal is to find the height&nbsp;h, which is the side opposite the given angle. First, we must identify the components of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-280967","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280967","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=280967"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280967\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280967"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}