Help With Physics Vector Problem

[physicsguy101]

Homework Statement

Someone bikes 3.7 km due west, and then 6.6 km at 57º west of north. The person continues for an unknown distance in an unknown direction. He ends up 2.3 km at 10º south of east of where he started.
Find the magnitude and specific direction of the third part of the person's trip.

Homework Equations

Ax = Acosθ
Ay = Asinθ
a2 + b2 = c2
tanθ = y/x

The Attempt at a Solution

I have a feeling that something isn't checking out. If someone can take a look over that work and see if I've gone wrong somewhere, that would be great.

Thanks in advance for the help!

 

[Mmm_Pasta]

I just did the problem. It is fine.