How far is the ship from the starting point and in what direction?

Question

A ship first sails N80°E for 120 nautical miles and the S 20°W for 200 nautical miles. How far is the ship, then, from the starting point and in what direction?

Answer 1

The picture above shows the ship’s navigation. The distance from the starting point is given by: √(120²+220²-2×120×220cos60)=20√91=190.79 miles (cosine rule).

The angle, x, of the direction of the endpoint is:

180-80-sin⁻¹(220sin60/190.79) (sine rule)=100-87=13º approx.

This is S13ºE.