This is an example of a problem from our Larson Calculus textbook (6th ed). Problem not my intellectual property, asking for educational purposes:

An airplane is traveling at a fixed altitude with a negligible wind factor. The airplane

is traveling at a speed of 500 miles per hour with a bearing of 330, as shown in

Figure 11.13(a). As the airplane reaches a certain point, it encounters wind with a

velocity of 70 miles per hour in the direction N 45 E ( 45 east of north), as shown in

Figure 11.13(b). What are the resultant speed and direction of the airplane?

In the solution, they set up the angles as 120 degrees and 45 degrees, without actually explaining why.

The answer was: The new speed of the airplane, as altered by the wind, is approximately 522.5 miles per

hour in a path that makes an angle of 112.6 with the positive x- axis.

Does anybody know why? I've been stuck on this problem for so many days!!