Law of Sines and alternate interior angles?

AI Thread Summary
The discussion revolves around a geometry problem involving two rangers spotting a fire from different towers. Ranger A observes the fire at 321 degrees, while Ranger B, located 60 miles away at a 47-degree angle from Ranger A, sees it at 279 degrees. The user initially calculates angle A as 86 degrees and angle C as 42 degrees, expressing confusion about the subtraction of angles and its relevance to alternate interior angles. Ultimately, the user resolves their confusion independently, indicating a successful understanding of the problem. The thread highlights the application of the Law of Sines in solving triangle-related problems in geometry.
benign.psycho
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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!
 
Last edited by a moderator:
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Nevermind, figured it out, feel stupid.

Heh.
 

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