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Two lookout stations, which are 25 miles apart along the coast on a north-south line, spot an approaching yacht. One lookout station measures the direction to the yacht at N 33degrees E, and the other station measures the direction of the yacht at S 62degress E. How far is the yacht from each lookout station? How far is the yacht from the coast?

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    Draw a diagram. If the northern station is at A, and the southern is at B, and the yacht is at C,

    angle C is 180-62-33 = 85°

    Using the law of sines,

    a/sin62° = b/sin33° = 25/sin85°
    a (distance from B) = 22.16
    b (distance from A) = 13.67
    distance from coast is a sin33° = b sin62° = 12.07

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