trigonometry

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as you walk on a straight level path toward a mountain, the measure of the angle of elevation to the peak from one point is 33 degrees. From a point 1000 feet closer, the angle of elevation is 35 feet. How high is the mountain?

  • trigonometry -

    as usual, draw a diagram. You will see that the height of the mountain obeys

    h/x = tan35
    h/(x+1000) = tan33

    so,

    h/tan33 = h/tan35 + 1000
    h/.6494 = h/.7002 + 1000
    h = 8951 ft

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