You kind of need the picture for this one, because while the instructions say that each of 2 towers A & B uses the other tower as its 0º, but instructions do not say which direction to use for measurements.
If all angles are all measured clockwise with respect to its respective 0º, the result is impossible… fire would be on 2 opposite sides of AB.
So tower A measures counter-clockwise from B, tower B measure clockwise from A… then all good.
To visualize: imagine horizontal distance between A and B, and fire F “above” (North?) segment AB somewhere.
image link (provided) — https://ibb.co/YByVKH6
Given: ∡FAB = 42º, ∡FBA = 64º, AB = 10 miles
Observations: Opposite side AB is ∠AFB = 180º - (42º + 64º) = 74º
Requested: side AF (opposite ∠FBA = 64º) [to nearest 1/10 th of a mile]
Law of Sines: AF/sin(64º) = AB/sin(74º) ==> AF = AB sin(64º)/sin(74º) = 10 sin(64º)/sin(74º) ==>
AF = 9.3 miles
