You will need to use knowledge of the sine and cosine functions from the acronym SOHCAHTOA. A bearing is an acute angle relative to the North/South line on a compass. Some examples are demonstrated below. ( see screenshot )

Explain how to solve each problem thoroughly, along with a thorough
explanation of the concepts used to solve each problem.

1. A car leaves a city at a bearing of N 50◦ E and travels in a straight line for 200 miles. How many miles north and how many miles east has the car traveled from the city?

2. A boat leaves an island and travels 36 miles at a bearing of N 53◦ E. Next, the boat makes a 90◦ clockwise turn and
travels 15 miles on a bearing of S 37◦ E.
(a) How far is the boat from the island?
(b) What is the bearing of the boat from the island?