{"id":203879,"date":"2025-03-21T02:30:01","date_gmt":"2025-03-21T02:30:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=203879"},"modified":"2025-03-21T02:30:05","modified_gmt":"2025-03-21T02:30:05","slug":"a-student-is-standing-20-feet-away-from-the-base-of-a-tree-he-looks-to-the-top-of-the-tree-at-a-50-angle-of-elevation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/21\/a-student-is-standing-20-feet-away-from-the-base-of-a-tree-he-looks-to-the-top-of-the-tree-at-a-50-angle-of-elevation\/","title":{"rendered":"A Student Is Standing 20 Feet Away From The Base Of A Tree. He Looks To The Top Of The Tree At A 50\u00b0 Angle Of Elevation"},"content":{"rendered":"\n

A Student Is Standing 20 Feet Away From The Base Of A Tree. He Looks To The Top Of The Tree At A 50\u00b0 Angle Of Elevation. His Eyes Are 5 Feet Above The Ground. Using Cos 50\u00b0 0.64, What Is The Height Of The Tree To The Nearest Foot? 350 36 Feet 24 Feet 29 Feet 31 Feet<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is 29 feet<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

We can solve this problem using trigonometry, specifically the tangent function, since we are dealing with a right triangle formed by the student, the tree, and the line of sight.<\/p>\n\n\n\n

Step 1: Define the Known Values<\/strong><\/h4>\n\n\n\n
    \n
  • The student is 20 feet<\/strong> away from the base of the tree.<\/li>\n\n\n\n
  • The angle of elevation to the top of the tree is 50\u00b0<\/strong>.<\/li>\n\n\n\n
  • The student\u2019s eye level is 5 feet above the ground<\/strong>.<\/li>\n<\/ul>\n\n\n\n

    Step 2: Set Up the Trigonometric Equation<\/strong><\/h4>\n\n\n\n

    We let h<\/strong> be the height of the tree above the student\u2019s eye level. The tangent function is used because we have the opposite and adjacent sides in the right triangle: tan\u2061(50\u2218)=oppositeadjacent\\tan(50^\\circ) = \\frac{\\text{opposite}}{\\text{adjacent}} tan\u2061(50\u2218)=h20\\tan(50^\\circ) = \\frac{h}{20}<\/p>\n\n\n\n

    From a calculator: tan\u2061(50\u2218)\u22481.19\\tan(50^\\circ) \\approx 1.19 1.19=h201.19 = \\frac{h}{20}<\/p>\n\n\n\n

    Step 3: Solve for h<\/strong><\/h4>\n\n\n\n

    Multiply both sides by 20: h=20\u00d71.19h = 20 \\times 1.19 h=23.8\u224824 feeth = 23.8 \\approx 24 \\text{ feet}<\/p>\n\n\n\n

    Step 4: Add the Student\u2019s Eye Height<\/strong><\/h4>\n\n\n\n

    The total height of the tree is: 24+5=29 feet24 + 5 = 29 \\text{ feet}<\/p>\n\n\n\n

    Thus, the correct answer is 29 feet<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Generated Image Description:<\/strong><\/h3>\n\n\n\n

    A student is standing on the ground, 20 feet away from a tall tree. A right triangle is formed by the student\u2019s eye level (5 feet above the ground), the top of the tree, and the base of the tree. A dotted line represents the student\u2019s line of sight at a 50\u00b0 angle to the top of the tree. The height of the tree is labeled as 29 feet<\/strong>.<\/p>\n\n\n\n

    Here is the generated image illustrating the problem. Let me know if you need any modifications or explanations!<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A Student Is Standing 20 Feet Away From The Base Of A Tree. He Looks To The Top Of The Tree At A 50\u00b0 Angle Of Elevation. His Eyes Are 5 Feet Above The Ground. Using Cos 50\u00b0 0.64, What Is The Height Of The Tree To The Nearest Foot? 350 36 Feet 24 Feet […]<\/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-203879","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203879","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=203879"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203879\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=203879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=203879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=203879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}