A fishing boat leaves port on a bearing of 35 degrees and travels 13.3 miles. The boat then turns due east and travels 4.0 miles.

Question

A fishing boat leaves port on a bearing of 35 degrees and travels 13.3 miles. The boat then turns due east and travels 4.0 miles. How far is the fishing boat from port and what is it bearing from port?

Answer 1

After the first leg, the boat's position is (13.3 * sin 35, 13.3 * cos 35).

 

After the second leg, the boat's position is (13.3 * sin 35 + 4, 13.3 * cos 35) = (11.63, 10.89)

 

So the magnitude of the second vector is √(11.63² + 10.89²) = √(135.2569 + 118.5921) = √253.849 = 15.93.

 

The angle between the x-axis and the vector is tan^-1 (10.89 / 11.63) = tan^-1 = 43.12°.  But the bearing is the angle between the Y-AXIS and the vector, which is 90° - 43.12° = 46.88°