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17 November, 13:11

A woman standing on a hill sees a flagpole that she knows is 35 ft tall. the angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. find her distance x from the pole. (round your answer to one decimal place.)

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  1. 17 November, 15:59
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    The top triangle has a vertical leg of "x", an angle opposed of 18 degrees, and a horizontal leg of d.

    So tan (18) = x/d

    and d = x/tan (18)

    The bottom triangle has a vertical leg of "35-x", an angle opposite of 14 deg. and a horizontal leg of "d".

    So tan (14) = (35-x) / d and d = (35-x) / tan (14)

    Solving for "d":

    x / tan (18) = (35-x) / tan14

    (tan14) x = 35tan18 - (tan18) x

    x (tan14 + tan18) = 35tan18

    x = 11.3722/0.5742

    x = 19.81 ft. (distance the lady is from the pole)
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