A helicopter flies from the airport on a course with a bearing of 19 degrees.

Question

After flying for 97 ​miles, the helicopter flies due east for some time. The helicopter flies back to the airport with a bearing of 225°.

How far did the helicopter fly on the final leg of its​ journey? in miles

Answer 1

Flying east is a bearing of 90°

Thus, we have a triangle with the three segments the plane flies.

Going from a bearing of 19° to 90° is a turn of 71°, which means the interior angle is 180° - 71° = 109°

Then, turning from 90° to 225° is a turn of 135°, which means the interior angle is 180° - 135° = 45°.

The length of 87 is opposite the 45° angle, and the final leg is opposite the 109° angle.

Thus, sin 45°/87 = sin 109°/b or b = 87 sin 109°/sin 45° = 116.33