In order to determine the distance between two aircraft a tr

In order to determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle alpha between them. Determine the distance between the planes when alpha = 25 degree, b = 69 miles, and c = 36 miles.

Solution

use cosine rule to find a:

a^2 = b^2+c^2 - 2bccos(alpha)

a^2 = 69^2 + 36^2 -2*69*36cos25

= 1554.4629

a = 39.43 miles