Posted by Sandy on Sunday, June 8, 2008 at 9:38pm.
A ranger in fire tower A spots a fire at a bearingof 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?

Principles of Math 11  Reiny, Monday, June 9, 2008 at 8:14am
I have tried to construct a diagram to match the information in your question, but was not able to do so.

Principles of Math 11  drwls, Monday, June 9, 2008 at 8:43am
I have attempted to draw the triangle ABF using your bearing information and the 45 mile distance from A to B (which I call side f). Vertex F is the location of the fire. I get a 30 degree angle at B, 110 at A and 40 at F. The law of sines can be used to obtain the two unknown sides. You are asked for the distance from A to F, which is side b.
b/sin 30 = 45/sin 40
b = (0.5000/0.6428)*45 = 35.00 miles
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