A plane flies due south for 600 miles. It turns and flies 250 miles, 35 degrees east of south. How far is the plane from its origin.
1) draw a picture to help determine the number of degrees in the angle between the 600 mi flight and the 250 mi flight
2) use the Law of Cosines.
The included angle we are looking for = 180 - 35 = 145°
Using the Law of Cosines the distance, D, from the origin is
D = sqrt ( 600^2 + 250^2 - 2 (600 * 250) cos (145° ) ) ≈ 817.5 miles
Here's a pic :