SOLUTION: I need help with the following question please. A ranger in a fire tower A spots a fire at a bearing of 295 degrees. A ranger in fire tower B, located 45 miles at a bearing o

Algebra ->  Trigonometry-basics -> SOLUTION: I need help with the following question please. A ranger in a fire tower A spots a fire at a bearing of 295 degrees. A ranger in fire tower B, located 45 miles at a bearing o      Log On


   

Question 144634: I need help with the following question please.
A ranger in a fire tower A spots a fire at a bearing of 295 degrees. A ranger in fire tower B, located 45 miles at a bearing of 45 degrees from Tower A, spots the same fire at a bearing of 255 degrees. How far away from Tower A is the fire?
Thanks very much.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the angles of the triangle formed by A, B and the fire. The angle at A is 110 degs, the angle at B is 30 degs, and the angle at the fire is 30 degs.
Using the law of sines, 45/sin(40) = x/(sin(30).
x = 45(sin(30))/sin(40)
x = 35.0038 miles.