Trigonometry Word Problem

Question

A ship leaves Miami and cruises for 74 mi on a bearing of S60°E. Another ship leaves at the same time and sails for 56 mi on a bearing of S20°E. How far apart are the two ships?

Answer 1

The angle between the paths formed by the ships with vertex at Miami is 40°. Let x be the distance between the ships.

By the Law of Cosines, x² = 56² + 74² - 2(56)(74)cos40°

x² = 8612 - 6348.9763

x = 47.6 miles