An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of 325°. What are the plane's actual speed and direction angle?

Tailwind component = 56 cos (35) = 46

cross wind component = 56 sin (35) = 32

course deviation = tan^-1 (32) / (286) = 6 degrees

116 degrees at 286 kts

this is actually a slight bit of shorthand.

slightly more precise is C^2 = 286^2 + 32^2

C = 288

and you could have used the law of cosines.