Question

A cargo vessel which has travelled 4 miles north was forced by a storm to hide temporarily in an island which is 5 miles northeast. Show these displacements graphically and find the resultant displacement.

Answer 1

The resultant displacement is the diagonal of the parallelogramm shown in the figure above. According to the law of cosines, the length of this diagonal is:

$$d = \sqrt{4^2 + 5^2 - 2\cdot 4\cdot 5\cos 135\degree} \approx 8.32\space miles$$

Answer. 8.32 miles.