An airplane is traveling at a speed of 200 miles/hour with a bearing of 240°. the wind velocity is 60 miles/hour at a bearing of 25°. what are the plane's actual speed and direction angle?

Vx=-200cos60+60cos25         

vy=-200sin60+60sin25
         
v=(vx^2+vy^2)^(1/2)

v=154.73mph

tana=vy/vx

a=arctan(vy/vx)

a≈72.85 and this is in the third quadrant so:

The bearing is 180+72.85=252.85

So:

The plane is traveling at a speed of 154.73mph with a bearing of 252.85°