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March 25, 2017

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When the sun's angle of elevation is 30 degree the shadow of a post is 6 ft longer than when the angle is 45
degree. find the height of the post

  • trig - ,

    let the height of the post be h ft, let the length of the shadow be x
    when angle is 45°, the height of the post and its shadow would be equal, so x = h at 45°

    at 30°, length of shadow = h+6

    tan 30 = h/(h+6)
    1/√3 = h/(h+6)
    √3h = h + 6
    √3h - h = 6
    h(√3 - 1) = 6
    h = 6/(√3 - 1) = appr. 8.2 ft
    √3h - h =

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