Theory question 112
BearingsTwo men P and Q set off from a base camp R prospecting for oil. P moves 20km on a bearing of 205° and Q moves 15km on bearing of 060°. Calculate the (a) distance of Q from P. (b) bearing of Q from P. (Give your answer in each case, correct to the nearest whole number).
Show the model answer
Sketch: from R, P is 20 km on 205° and Q is 15 km on 060°; <PRQ = 205° − 60° = 145°.
(a) Cosine rule: PQ2 = 202 + 152 − 2(20)(15) cos 145° = 625 + 600 × 0.8192 = 1116.5. PQ = 33.4 ≈ 33 km.
(b) Sine rule in triangle PRQ: sin <RPQ = 15 sin 145°/33.41 = 0.2575, so <RPQ ≈ 14.9°.
The bearing of R from P is 205° − 180° = 025°, so the bearing of Q from P = 025° + 14.9° ≈ 040°.
Find the angle at R from the two bearings, then use the cosine rule for the distance and the sine rule for the angle at P.