Two fire towers, A and B, are 20.3 km apart. From tower A, the bearing of tower B is 70̊. The ranger in each tower observes a fire and radios the bearing of the fire from the tower. The bearing from tower A is 25̊ and from tower B is 345̊. How far is the fire from each tower?

Answer 1

triangle A B F
North to AB = 70
North to AF = 25
so
angle FAB = 70-25 = 45
North to BF = 345 clockwise so 15 counterclockwise
so exterior angle AB to BF = 70 +15 = 85
so
angle ABF = 180 -85 = 95
that leaves angle AFB = 180 -45-95 = 40
then
sin 40/20.5 = sin 95/af = sin 45/bf

Answer 2

ohh thanks