Question

A jet skier departs from Pier 1, travels 796 meters directly to a buoy, makes a turn, and travels 1054 meters directly to Pier 2, which is 411 meters from Pier 1.

How many degrees was the jet skier's turn?

Round your answer to the nearest whole degree.

Answer 1

9514 1404 393

Answer:

160°

Explanation:

The path is a triangle with side lengths 796, 1054, and 411 meters. The turn is opposite the short side. The interior angle of the triangle at that point can be computed using the law of cosines. If we label the sides a, b, c, respectively, then ...

c² = a² + b² - 2ab·cos(C)

C = arccos((a² +b² -c²)/(2ab)) = arccos(1575611/1677968) ≈ 20.116°

The external angle at the buoy is 180° -20° = 160°.

The jet skier's turn was about 160°.