Question

Two ships leave a Port O. One ship travels on a bearing of 340 to a point P which is 50 km from O. The other ship travels on a bearing of 060 to a point Q, 85 km from O.

(A) Draw a diagram to represent the position of the port and the two ships. On your diagram, carefully label North, the given angles and the distances travelled.
(B) Calculate the distance PQ in km
(C) Determine the bearing of P from Q.

Answer 1

(a) The diagram of the position of the port and the two ships is in the image attached.

(b) The distance PQ in the diagram is 90.82 km

(c) The bearing of P from Q is 272.8⁰.

How to calculate the distance PQ?

(b) The distance PQ in the diagram is calculated by applying the following formula as follows;

PQ² = PO² + QO² - 2(PO x QO) cos (O)

y² = 50² + 85² - 2(50 x 85) x cos(80)

y² = 8,248.99

y = √ (8,248.99)

y = 90.82 km

(c) The bearing of P from Q is calculated as follows;

bearing = θ + 60 + 180

The value of angle θ is calculated as;

sin θ / 50 = sin 80 / 90.82

sin θ = 0.5422

θ = arc sin (0.5422)

θ = 32.8⁰

bearing = 32.8 + 60 + 180

bearing = 272.8⁰