Question

A pilot flies in a straight path for 1 hour and 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. if she maintains a constant speed of 685 miles per hour, how far is she from her starting position?

Answer 1

The pilot makes a big triangle with her flight path. The longest side will be her distance from the start as the crow flies.

Use the Law of Cosines (deg mode on a calculator):

c^2 = a^2 + b^2 - 2ab(cos C)

C = 170 degrees (only a 10 deg correction from 180)

a = 685 x 1.5 = 1027.5 miles

b = 685 x 2 = 1370 miles

It doesn’t matter which side is a and which side is b.

Now plug in the values and solve for c. Hope this helps.