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The angle of elevation from point A to the top of a vertical pole is 30.0 degrees. At point B, 6 meters closer to the base of the pole and on a line through the base of the pole and point A, the angle of elevation to the top of the pole is 37.0 degrees. Find the height ( to the nearest tenth of a foot) of the pole.

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    Let X be the distance from the closer point B) to the pole.
    Let H be the height of the pole. You have two equations in two unknowns.

    H/X = tan 37 = 0.75355
    H/(X+6) = tan 30 = 0.57735
    (X+6)/X = 1.3052 = 1 + 6/X
    6/X = 0.3052
    X = 19.66 m
    H = 0.75355X = 14.8 m

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