Three points P, Q and R are on a level ground. Q is 240m from P on a bearing of 230°. R is 120m to the east of P.

Question

(a) Using a scale of 1cm to represent 40m, draw a diagram to show the positions of P, Q and R in the space provided below.
(b) Determine :

(i) the distance of R from Q;
(ii) the bearing of R from Q

(c) A vertical post stands at P and another one at Q. A bird tales 18 seconds to fly directly from the top of the post at Q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 9°

Calculate;
(i) The distance, to the nearest meter, the bird covers;
(ii) The speed of the bird in km/h

Answer 1

if P is at (0,0), then we have
Q: (-184,-154)
R: (120,0)

so, RQ = 341
bearing = 180° + arctan(304/154) = 243°

Answer 2

d = 341/cos9° = 345m
speed = 345m/18s * 1km/1000m * 3600s/hr = 69km/hr