Question

two fire lookout stations are 12 miles apart, with station B directly west of station A. Both stations spot a fire. The bearing of the fire from station A is S30 W and the bearing of the fire from ststaion B is S42 E. How far is the fire from each lookout station?

Answer 1

angle of depression from a to fire is 90-30=60 from east-west horizontal

angle of depression from b to fire is 90-42=48 from east-west horizontal

So the angle from fire adjacent to the east-west horizontal is 180-60-48=72

Now we can use the law of sines to solve for the distances...

sin72/12mi=sin48/A=sin60/B

A=12sin48/sin72=9.38mi

B=12sin60/sin72=10.93mi