Theory question 110
BearingsIn a town, Chief X resides 60 m away on a bearing of 057° from the palace P. While Chief Y resides on a bearing of 150° from the same palace P. The residence of X and Y are 180 m apart.
(a) Illustrate the information in a diagram.
(b) Find, correct to three significant figures, the: (i) bearing of X from Y; (ii) distance between P and Y.
Show the model answer
Model answer
(a) From P, PX = 60 m on 057° and PY on 150°; ∠XPY = 150° − 57° = 93°; XY = 180 m
(b)(i) Sine rule: sin ∠PYX = 60 sin 93° ÷ 180 ≈ 0.3329 ⇒ ∠PYX ≈ 19.4°. Bearing of P from Y = 330°, so bearing of X from Y = 330° + 19.4° ≈ 349°
(ii) ∠PXY = 180° − 93° − 19.4° = 67.6°; PY = 180 sin 67.6° ÷ sin 93° ≈ 167 m (166.6 m)
Explanation
Find the angle at P first: 150° − 57° = 93°.