Law of Cosines Trigonometry

Question

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 695 mi/h, how far is she from her starting position?

Your answer is_______ miles?

Answer 1

Let's denote the distance the pilot flew in her original direction as "d", then the distance she flew after the course correction is "695*2 = 1390" miles, and the angle between the two directions is 180-10 = 170 degrees.

Using the Law of Cosines, we can find the distance between the starting point and the final position:

d² = 1390² + 695² - 2*1390*695*cos(170) d² = 1936875 d =√(1936875) d ≈ 1391.7 miles

Therefore, the pilot is about 1391.7 miles away from her starting position.