Arpan S. answered • 06/27/21

Science Expert(Mathematics, Physics, Chemistry)

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**.