bearing and distance

Two vehicles p and q leave a station at the same time.p travels 8km/hour on a bearing of 025 degree and q 5km/hour on a bearing of 45 degree west of north.how far apart are they and what is the bearing of p from q after 3hours?

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asked by mary
  1. Use the law of cosines. After t hours, the distance d between the vehicles is

    d^2 = (8t)^2 + (5t)^2 - 2(8t)(5t)cos70°

    because the angle between the bearings if 25+45 = 70°

    So, just plug in t=3 and solve for d.

    As for the bearing from q to p, just find the slope of the line joining p and q. The angle with that slope is θ, and the bearing is 90-θ degrees east of north.

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    posted by Steve

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