An airplane is flying in a direction of 65 degrees at 450 mph. A wind is blowing in a direction of 20 degrees at 35 mph. Find the actual speed and direction of the plane.

Answer 1

You don't say whether these are courses from due North, or from the positive x-axis. I'll do the latter.

the x- and y-components of the vectors are

(450 cos65°, 450 sin65°) = (190.18,407.84)
(35 cos20°, 35 sin20°) = (32.89, 11.97)

Add them up to get
(223.07,410.81) = 475 mph at 61°