trip application problem

Question

A ship is sailing due north. At a certain point the bearing of a lighthouse that is 20 miles away is found to be 33 degrees east of due north. Later, the bearing is determined to be 54 degrees east of due north. How far, to the nearest tenth of a mile, has the ship traveled?

Answer 1

In triangle ABL, A is the point at which the ship is 20 miles from the lighthouse, L, and the bearing is N33E (angle A). AL=20 miles.

The ship travels to B where L is now N54E. The exterior angle of a triangle (54º) is the sum of the two opposite interior angles A(=33º) and L, so L=54-33=21º. Using the sine rule AB/sin21=20/sin(180-54)=20/sin54=24.72 approx.

Therefore AB, the distance the ship has travelled, is 24.72sin21=8.86 miles approx. That is 8.9 miles to the nearest tenth of a mile.