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8 August, 23:47

A guy wire makes a 67° angle with the ground. Walking out 32 feet further from the tower, the angle of elevation to the top of the tower is 39°. Find the height of the tower.

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  1. 8 August, 23:59
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    This is the theory of geometry, the height of the tower will be given by:

    tan theta=[opposite]/[adjacent]

    let the opposite be h;

    adjacent be x;

    tan 67=h/x

    thus;

    h=xtan67

    also

    tan39=h / (x+32)

    h = (x+32) tan39

    xtan67 = (x+32) tan39

    2.4x = (x+32) 0.8

    2.4x=0.8x+25.6

    2.4x-0.8x=25.6

    1.6x=25.6

    x=25.6/1.6

    x=16 ft

    thus

    h=xtan67

    h=16tan67

    h=37.7 ft
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