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trigonometry

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a surveyor finds that from Point A on the ground the angle of elevation to the top of a mountin is 23 degrees. when he is at point B that is 1/4 closer to the base of the mountain the angle of elevation is 43 degrees. how high is the moutnain? One mile =5280 feet. (Assume that thr base of the mountain and the two observation points are on the same line.)Give answer to the nearest foot.

  • trigonometry -

    tan23 = Y/X,
    Y = Xtan23,

    tan43 = Y/(X-.25).
    Y = (X-0.25)tan43.

    y = Xtan23 = (X-0.25)tan43,
    Xtan23 = (X-0.25)tan43,
    Xtan23 = Xtan43-0.25tan43,
    0.4245X = 0.9325X-0.2331,
    0.4245X-0.9325X = -0.2331,
    -0.508X = -0.2331,
    X = 0.4589 Miles.

    y = 0.4589tan23 = 0.1948 miles.

    Y = 0.1948mi * 5280ft/mi = 1029 Ft.
    = Height of mountain.

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