# Trigonometry (Law of Sine)

posted by Alianne

Fire towers A and B are located 10 miles apart. They use the direction of the other tower as
0°. Rangers at fire tower A spots a fire at 42°, and rangers at fire tower B spot the same fire
at 64°. How far from tower A is the fire to the nearest tenth of a mile?

1. Reiny

Your wording of the question is confusing, but I think I see a triangel FAB, where AB = 10
angle A = 42° and angle B = 64°

then angle F = 180-64-42 = 74°
FA/sin64 = 10/sin74
FA = 10sin64/sin74 = appr 9.4 miles

2. ttyyttyytyt

9.3 miles

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