Answer to Question #93300 in Trigonometry for Precious

Question #93300
Two ships P and Q left a port R at the same time on different routes. Q sailed on a bearing of 150° while P sailed on the north side of Q.After a distance of 8km and 10 km by p anq respectively their distance apart was 12km. Find the bearing of P from R.
1
Expert's answer
2019-08-26T09:17:40-0400

Find the angle "x" between RP and RQ using the law of cosines:


"PQ^2=RP^2+RQ^2-2RP\\cdot RQ\\cdot cos x""cos x=\\frac{RP^2+RQ^2-PQ^2}{2RP\\cdot RQ}""cos x=\\frac{8^2+10^2-12^2}{2\\cdot 8\\cdot 10}=\\frac{64+100-144}{160}=\\frac{20}{160}=\\frac{1}{8}"

"x\\approx 83\\degree"

Then the  bearing of P from R is:


"150\\degree-83\\degree=67\\degree"


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