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6 February, 18:35

A person whose eye level is 20 feet above the ground is looking at a building. The angle of elevation to the top of the building is 31º and the angle of depression to the bottom of the building is 24∘. What is the height (in feet) of the building? Round your answer to the nearest foot.

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  1. 6 February, 18:45
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    Distance of the person from the building (x)

    tan 24 = 20/x = > x = 20/tan 24 = 44.92 ft

    The height of the building above the height of the person and the distance of the person from the building forms two legs of right angled triangle.

    Therefore, if h is the height of the building, then;

    tan 31 = (h-20) / 44.92

    h-20 = 44.92 tan 31

    h = (44.92 tan 31) + 20 = 26.99 + 20 = 46.99 ft
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