Question

From a fire tower, A, a fire is spotted on a bearing of N42°E. From a second tower, B, the fire is on a bearing of N12°W. The two fire towers are 23 km apart, and A is N63°W of B. How far is the fire from each tower?

Just need help interpreting the diagram from the question. Thank you in advanced.

Answer 1

My diagram has triangle ABF, with F as the fire.
angle A = 75°, angle B = 51° and angle F = 180-75-51 = 54°
also AB = 23 km

so you use the sine law to find the other two sides,
first one: AF/sin51 = 23/sin54
AF = 23sin51/sin54 = 22.09 km

find BF in a similar way.

Answer 2

thanks so much!

Answer 3

Why A=75°