A boat leaves the entrance to a harbor and travels 125 miles

A boat leaves the entrance to a harbor and travels 125 miles on a bearing of N 52 degree E. How many miles north and how many miles east from the harbor has the boat traveled? The boat has traveled ____ miles north. (Round to the nearest tenth of a mile.) The boat has traveled ____ miles east. (Round to the nearest tenth of a mile.)

Solution

The angle N52^oE means that the direction is 52^o East of North.

so, the distance traveled in North is: 125cos52 = 77.0 miles.

and distance traveled in East is: 125sin52 = 98.5 miles.