Theory question 111
BearingsThree towns P, Q and R are such that the distance between P and Q is 50km and the distance between P and R is 90km. If the bearing of Q from P is 075° and the bearing of R from P is 310°, find the: (a) distance between Q and R; (b) bearing of R and Q.
Show the model answer
Model answer
(a) ∠QPR = 75° + (360° − 310°) = 125°
Cosine rule: QR2 = 502 + 902 − 2 × 50 × 90 × cos 125° = 10600 + 5162 = 15762
QR ≈ 125.5 km
(b) Sine rule: sin ∠PQR = 90 × sin 125° ÷ 125.5 = 0.5873, so ∠PQR ≈ 36.0°
Bearing of P from Q = 075° + 180° = 255°
Bearing of R from Q = 255° + 36° = 291°
Explanation
Find the angle between the two bearings first, then use the cosine rule.