Question

The boundaries PQ, QR, RS and SP of a ranch are straight lines such that: Q is 16km on a bearing of 040° from P, R is directly south of Q and east of P and S is 12km on a bearing of 120° from R.

(b) From the scale drawing determine:
(i) The distance, in kilometers, of P from S
(ii) The bearing bf P from S

(c) Calculate the area of the ranch PQRS in square kilometers.

Answer 1

Did you make a drawing?
PR = 16 cos50° = 10.28
(i) PS^2 = PR^2 + 12^2 - 2*PR*12*cos150°
PS = 21.53
(ii) In triangle PRS, angle P is found by
sinP/12 = sin150°/21.53
The bearing of S from P is 90°+angle P

Answer 2

Thanks