Bearings Problem Solving Question

Question

From a lighthouse two boats can be sighted. Boat 1 on a bearing of 60° at a distance of 2km and Boat 2 on a bearing of 340° at a distance of 3km.

a) If Boat 1 is in need of assistance, what bearing would Boat 2 need to travel on to reach it?

b) Assuming Boat 1 does not move, how far would Boat 2 have to travel?

Answer 1

In (N, E) coordinates, Boat 1 is located

relative to the lighthouse at ...

2(cos(60°), sin(60°)) = (1.0, 1.732).....

km

Boat 2 is located at ...

3(cost(340°), sin(340°)) = (2.819, -1.026).......km

So, relative to Boat 2, Boat 1 is located at ...

(1, 1.732) -(2.819, -1.026) = (-1.819, 2.758).....km

This is at a bearing of ...

arctan(2.758/-1.819) = 123.4°

and a distance of ...

√(1.819² +2.758²)≈ 3.304.... km

a) Boat 2 would need to travel on a bearing of 123.4°.

b) Boat 2 would need to travel 3.3 km.