a fire (F) is spotted from two fire lookout station, A and B, which are located 12.3 miles apart. If station B reports the fire at angle ABF=52.8 degrees, and station A reports the fire at angle BAF = 24.7 degrees. How far is the fire from station A and how far is the fire from station B?

Question

a fire (F) is spotted from two fire lookout station, A and B, which are located 12.3 miles apart. If station B reports the fire at angle ABF=52.8 degrees, and station A reports the fire at angle BAF = 24.7 degrees.       How far is the fire from station A and how far is the fire from station B?

campbell_st · Answer

draw a diagram 

|dw:1406268478355:dw|

find angle F but angle sum of a triangle. 

then use the law of sines to find the length of AF

then the law of sines to find BF

hope it helps

anonymous · Answer

it does thank you, F = 102.5
B=12.3(sin58.8)/sin102.5