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It is 4.7km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73E. A ship has sailed due west from the port and its bearing from the lighthouse is N31E. How far has the ship sailed from the port?

  • trig -

    If the ship has sailed to point C,
    angle A = 73°-31° = 42°
    angle B = 17°
    so, angle C is 121°

    the distance AC is side a, where

    a/sin42° = 4.7/sin121°
    a = 3.67

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