{"id":161043,"date":"2024-11-03T20:50:28","date_gmt":"2024-11-03T20:50:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=161043"},"modified":"2024-11-03T20:50:30","modified_gmt":"2024-11-03T20:50:30","slug":"the-angle-of-elevation-from-l-to-k-measures-24-degrees","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/the-angle-of-elevation-from-l-to-k-measures-24-degrees\/","title":{"rendered":"The angle of elevation from L to K measures 24 degrees."},"content":{"rendered":"\n

The angle of elevation from L to K measures 24 degrees. If KL = 19, find JL.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find ( JL ) in the triangle ( JKL ) where ( L ) is the point of observation, ( K ) is the point above ( L ) at an angle of elevation of ( 24^\\circ ), and ( KL = 19 ), we can utilize trigonometric principles.<\/p>\n\n\n\n

Step-by-step Solution<\/h3>\n\n\n\n
    \n
  1. Identify the Right Triangle<\/strong>: The triangle formed by points ( J ), ( K ), and ( L ) is a right triangle. Here, ( KL ) is the vertical side, ( JL ) is the horizontal side, and ( JK ) is the hypotenuse.<\/li>\n\n\n\n
  2. Label the Triangle<\/strong>:<\/li>\n<\/ol>\n\n\n\n
      \n
    • ( K ): The top point directly above ( L ).<\/li>\n\n\n\n
    • ( L ): The point of observation at ground level.<\/li>\n\n\n\n
    • ( J ): The point where the horizontal distance ( JL ) extends.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Apply the Trigonometric Function<\/strong>: Since we know the angle of elevation ( \\angle K ) and the length of ( KL ), we can use the tangent function, which relates the angle to the opposite side (height, ( KL )) and adjacent side (base, ( JL )):
        [
        \\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}} = \\frac{KL}{JL}
        ]<\/li>\n\n\n\n
      2. Substituting Values<\/strong>: Given ( KL = 19 ) and ( \\theta = 24^\\circ ):
        [
        \\tan(24^\\circ) = \\frac{19}{JL}
        ]<\/li>\n\n\n\n
      3. Calculating JL<\/strong>: Rearranging the equation to solve for ( JL ):
        [
        JL = \\frac{19}{\\tan(24^\\circ)}
        ]<\/li>\n\n\n\n
      4. Using a Calculator<\/strong>:<\/li>\n<\/ol>\n\n\n\n
          \n
        • First, calculate ( \\tan(24^\\circ) ), which is approximately ( 0.4452 ).<\/li>\n\n\n\n
        • Substitute this value into the equation:
          [
          JL = \\frac{19}{0.4452} \\approx 42.6
          ]<\/li>\n<\/ul>\n\n\n\n

          Conclusion<\/h3>\n\n\n\n

          Therefore, the length of ( JL ) is approximately ( 42.6 ) units. This calculation provides an understanding of how trigonometry can be applied to real-world problems involving angles of elevation and horizontal distances. The tangent function is particularly useful when determining unknown lengths in right triangles where angles and one side are known.<\/p>\n\n\n\n

          In summary, by using trigonometric principles and the properties of right triangles, we have effectively calculated the distance ( JL ) based on the given angle of elevation and the height above the point of observation.<\/p>\n","protected":false},"excerpt":{"rendered":"

          The angle of elevation from L to K measures 24 degrees. If KL = 19, find JL. The Correct Answer and Explanation is: To find ( JL ) in the triangle ( JKL ) where ( L ) is the point of observation, ( K ) is the point above ( L ) at an […]<\/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-161043","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161043","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=161043"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161043\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}