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Trigonometry to find speed and distance

1. A car traveling due west is sighted 2 km directly north of a radar outpost. 10 minutes later, its bearing is N 78° 30' W. find the speed of the car per hour.

2. A boat is 25 km due west of a lighthouse A and lighthouse B is 15 km due north of lighthouse A. find the distance LH B to the boat and the bearing of LH B from the boat.

Solution Preview

(1) Let R be the radar outpost. Let the car be initially be at point P and move to point Q after 10 minutes (1/6 hour)

P is directly along north of R. Angle RPQ = 90 deg and angle QRP = 78 ...

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