Law of Sines and alternate interior angles?

[benign.psycho]

Homework Statement

A ranger in tower A spots a fire at a direction of 321 degrees. A ranger in tower B, located 60 mi at a direction of 47 degrees from tower A, spots the fire at a direction of 279 degrees. How far from tower A is the fire? How far from tower B?

Homework Equations

http://img19.imageshack.us/img19/9529/triangle.jpg

The Attempt at a Solution

Angle A is 86 degrees. From here, I'm not exactly sure how to get the solution. I know that angle C is given from (321 degrees - 279 degrees), which is 42 degrees. Once I have angle C, I can solve for everything else.

I know this has something to do with alternate interior angles, but can't quite grasp why the subtraction is taking place. On another problem similar to this, I'm even more confused because the subtraction yields nothing of importance.

Can you guys explain this clearly for me, any rules or laws that are used here?

Thanks!

 

[benign.psycho]

Nevermind, figured it out, feel stupid.

Heh.