A jogger runs at a constant speed of one mile every 8 minutes in the direction S50°E for 24 minutes and then in the direction N17°E for the next 17 minutes.

Question

A jogger runs at a constant speed of one mile every 8 minutes in the direction S50°E for 24 minutes and then in the direction N17°E for the next 17 minutes. Approximate, to the nearest tenth of a mile, the straight-line distance from the endpoint to the starting point of the jogger's course.

________ mi

Answer 1

Draw and label all angles and distances

d represents the distance to the starting point

The angle at the turn measures 67º

Use the Law of Cosines

d² = 192² + 132² - (2)(192)(132) cos 67°

Can you calculate and answer?

Answer 2

By the way, in the video, the reason why the angle is 67 degrees is that the angle on the inside of the triangle is the suppliment of the angle on the outside of the triangle.