A pilot flies in a straight path from 1 h 30 min She then ma

A pilot flies in a straight path from 1 h 30 min. She then makes a course correction, heading 12 degree to the right of her original course, and 2 h in the new direction. If she maintains a constant speed of 775 mi/h, how far is she from her starting position? (Round your answer to the nearest mile.) mi

Solution

1st leg = 1.5 x 775 = 1162.5 mi
2nd leg = 2 x 775 = 1550
included angle = 170 degrees
Using the law of cosines we get
The side opposite the 170 degree angle is the distance we want i.e.
a² = b² + c² - 2bc Cos(A)
a² = 1162.5² + 1550² -2 x 1162.5 x 1550Cos(170)
Solve for \"a\" we get

a²= 1351406.25 + 2402500 - 2325 x 1550 x 0.938

a²= 373588.75

we get a = 611 (approx)

I calculated this taking angle 10 degree as image is not too clear.