Non-Right Triangles: Law of Cosines

Question

A pilot flies in a straight path for 1 hour 15 minutes. She then makes a course correction, heading 55 degrees to the right of her original course, and flies 2 hours 45 minutes in the new direction. If she maintains a constant speed of 275 mi/h, how far is she from her starting position? Give your answer to the nearest mile.

She is  ___miles from her starting position

Answer 1

15 minutes =1/4 hour, and 45 minutes = 3/4 hours. Thus, the pilot travels 1 1/4 hours at 275 mph, turns 55°, and travels 2 3/4 hours for 275 mph.

275 * 1 1/4 = 343.75

275 * 2 3/4 = 756.25

As the turn is 55°, the angle is 125°

Then, the third side has length √(343.75² + 756.25² -2(343.75)(756.25)cos(125°)) = 994