Sine alpha = sqrt3/2, pi/2 < alpha < pi => alpha = 2pi/3

Cos beta = 1/2, 3pi/2 < beta < 2pi => beta = 5pi/3

I have attempted the problem in the image attached to this post but am wondering if someone could look over it and let me know if it is in fact correct?

Below is my work process in figuring out the answer:

http://i953.photobucket.com/albums/a...ig/Test4Q2.jpg