Finding Velocity and Direction in a Crosswind: Aircraft Navigation Problem

[LastBloomingFlower]

Ok, here's the problem.. What am I doing wrong??

The pilot of an aircraft wishes to fly due west in a wind blwoing at 50 km/h toward the south. If the speed of the aircraft in the absence of wind is 200 km/h, in what durection should the aircraft head and what should its speed be relative to the ground?

I keep getting Velocity of 216 and 14.05 direction and its not right??!? HELP!

 

[Astronuc]

To fly west, the plane must have a west component, and there must be a northern velocity component to offset the southbound wind.

Take the planes velocity magnitdue to be 200, which must be at some angle west of north (to offset the wind).

So 200*f(a) = 50, where f is some trig function and a is the angle.

 

[LastBloomingFlower]

I still can't get the right answer...

 

[Harmony]

By any chance, is the answer 14.48 degree and 193.6km/h?