Question

A boy walks 6 km from a point P to a point Q on a bearing of 065. He then walks to a point R at a distance of 13 km on a bearing of 146.

(1) sketch the diagram of his movements (2) calculate correct to the nearest kilometre, the distance PR​

Answer 1

9514 1404 393

Answer:

1. see below for a sketch
2. 12 km

Explanation:

The distance can be calculated using the Law of Cosines. The angle internal to the triangle at Q is (180°-(146° -65°)) = 99°. Then the distance PR can be found from ...

PR² = PQ² +QR² -2·PQ·QR·cos(∠PQR)

PR² = 6² +10² -2·6·10·cos(99°) ≈ 154.77

PR ≈ √154.77 ≈ 12.44 . . . . km

The distance PR is about 12 km.