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From the top of a 50m high bridge, two boats are seen at anchor. One boat is S 50degrees W and has an angle of depression of 38 degrees. The other boat is S 60degrees E and has a 35 degree angle of depression. How far apart are the boats?

  • Math -

    We draw 2 rt triangles with a common ver side:

    1. Draw a rectangle with the long sides hor.

    2. Draw a diagonal from the upper rt
    corner to the lower lt corner. This is
    the hyp of the larger triangle.The angle bet. the hyp and hor is 35 deg.

    3. Draw a 2nd hyp from the upper rt corner to a 2nd point on the hor side.
    This is the hyp of the smaller triangle. The dist. bet. the 2 hyp(d1)
    is the dist. bet. the 2 boats. The dist
    bet. the 2nd hyp and the ver side is d2. The angle bet. the 2nd hyp and hor
    is 38 deg.

    d1 + d2 = d = total dist. from the
    bridge.

    tan38 = 50/d2,
    d2 = 50/tan38 = 64m.

    tan35 = 50/(d1+d2),
    d1+d2 = 50/tan35 = 71.4m.

    d1 + d2 = 71.4,
    d1 = 71.4 - d2 = 71.4 - 64 = 7.4m = dist. bet. boats.

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