Math Solution and Explanation

Question

At 9am, a certain boat left a port in the direction of 50° east of north and maintains a speed of 90kph. At that same time, another boat left the same port in the direction of 30° east of south. How far apart were the two boats, two hours after they left the port?

Answer 1

>> I will ASSUME that the other boat also moves at the same speed. If not, substitute its actual speed in the following <<

Make a sketch with one vector 50° E of N or 40° above positive x axis, and second vector 30° E of S or 60° below the positive x axis. Let d be the length of the line connecting the tips of the two vectors. This forms a non-right triangle with the angle from port between the boats being 100° and the two lengths from port being (90 km/h)*(2 h) = 180 km.

The Law of Cosines works here: d² = 180² + 180² - 2(180)(180) cos 100° = 76,052, from which d = 276 km.