Law of Sines and Law of Cosines help

[Kimisaishime]

Homework Statement

Ok the problem states Station A observes the fire at an angel of 52 and station B spots the fire at an angle of 41. The stations are 17 mi. apart. Find the distance along the line of sight from the fire to the station that is closest to the fire.

I'm confused I don't hink I have enough to do the Law of Cosines, but I also feel that I don't have enough to do the Law of Sines. I am so confused do I need to do something else. Like do I need to use the distance equation along with the the Law of Sines or the Law of Cosines. Or do I need to do something different entirely.

Homework Equations

The Attempt at a Solution

 

[symbolipoint]

Do you need to solve the problem in two different ways? I see direct possibility for Law Of Sines.

Your problem description conforms to a triangle, base points A and B. AB is 11 miles; Angle at B is 41 degrees; angle at A is 128 degrees (do you see why?); the angle opposite AB is 11 degrees (now, do you see why this too?)

You know all three angles and you know only one side (AB); you just want to know the the side that goes from the point opposite of AB to the point A.