trigonometry

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two points, A and B, are 526 meters apart on a level strecth of road leading to a hill. The angle of elevation of the hilltop from A is 26deg30mins, and the angle of elevation from B is 36deg40mins. How high is the hill?

  • trigonometry -

    let c = distance from A to top
    angle opposite c = 180 -36.67 = 143.33
    angle oposite 526 = 180 - 143.33-26.5 = 10.17
    law of sines
    sin 10.17/526 = sin 143.33/a
    so a = 1779
    now
    sin 26.5 = h/1779
    h = 794

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