Solving the Direction of an Airplane Flying in the Wind

[Lazz72]

Here's the problem: An airplane is flying on a bearing of 340 degrees at 325 mph. A wind is blowing with the bearing of 320 degrees at 40 mph.

a) Find the component form of the velocity of the airplane.
b) Find the actual ground speed and direction of plane.

I can find the component form for the velocity of the airplane and the actual ground speed for the plane, but I don't know how to find the direction. I know it's a certain formula I don't know. Could someone please explain how to find the direction of the plane?

 

[willem2]

If you can find the ground speed of the plane you apparently know that

$$v_x = v \cos {\phi}$$

and

$$v_y = v \sin {\phi}$$

now if you divide those equations ...

for an airplane the x direction is to the north and the y direction to the east.