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

Question

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

(b) Determine
(i) The distance R from Q;
(ii) The bearing of R form Q.
(c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at Q to the pot of the post at P. Given that the angle of depression of the top of the post at P from the top of 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

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Answer 2

b. All angles are measured CW from +y-axis.
Given: PQ = 240m[230o].
PR = 120m[90o].
QR = ?

PQ + QR = PR.
QR = PR - PQ,
QR = 120[90o] - 240[230o],
QR = (120*sin90+240*sin230) + (120*Cos90+240*Cos230)I,
(i). QR = -63.9 - 154.3i = 167m.[22.5o] W. of S.
(ii). 22.5o W. of S. = 202.5o CW(bearing).

Answer 3

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