A boat sails 40km from point A to point B, east of A on a lake. Lodge P is south of point A. Another lodge Q is south of point B. The bearing of Q from point A is S52degresE and the bearing of P from B is S39degresW.

Question

A boat sails 40km from point A to point B, east of A on a lake. Lodge P is south of point A. Another lodge Q is south of point B. The bearing of Q from point A is S52degresE and the bearing of P from B is S39degresW.
If P is 60km from Q, calculate the bearing of lodge Q from lodge P.

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Damon · Answer

tan(90-39) = AP/40 so AP = 49.4 tan (90-52) = BQ/40 so BQ = 31.2 so P is (49.4-31.2) or 18.1 km south of Q and 40 km west of q tan theta = 40/18.1 theta = 65.7 degrees east of north from P to Q