The bearing of P from Q is 140degree and that of X from P is 315degree. If |PQ|=36km, and |PX|=55km, find |QX| and the bearing of Q from X.

Answer 1

since Q to P is 140°, P to Q is 320°
P to X is 315°, so angle QPX is 5°

using the law of cosines,

|QX|^2 = 36^2 + 55^2 - 2*36*55*cos5° = 376.1
So, |QX| = 19.39 km

55^2 = 19.39^2 + 36^2 - 2*19.39*36*cosQ
So, Q = 165.7°

The bearing of X from Q is thus

140+165.7 = 305.7°

Answer 2

sorry - you wanted the bearing of Q from X. Just subtract 180°.