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March 29, 2017

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A woman standing on a hill sees a flagpole that she knows is 65 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.)

  • trig - ,

    Draw the woman on the hill with her line of sight touching the pole somewhere in the middle.
    label her line of sight x, the top part of the pole h and the bottom part of the pole 65-h
    You now have 2 right-angled triangles
    for the top one:
    tan18° = h/x
    h = xtan18

    for the bottom part:
    tan14 = (65-h)/x
    xtan14 = 65-h
    h = 65 - xtan14

    then xtan18 = 65 - xtan14
    xtan18 - xtan14 = 65
    x(tan18-tan14) = 65
    x = 65/(tan18+tan14) = 113.2

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