Fire towers A and B are located 15 miles apart. Rangers at fire tower A spot a fire at
32°, and rangers at fire tower B spot the same fire at 63º. How far from tower B is the
fire to the nearest mile?
A.7
B.8
C.9
D.5

We assume the angles given are measured from the other tower to the fire, so they are angles internal to the triangle formed by the two towers and the fire.

Given two angles and one side, other side lengths can be found from the Law of Sines. It tells us ...

a/sin(A) = c/sin(C)

Angle C, the angle between towers A and B as measured at the fire, will be ...

180° -32° -63° = 85°

Then the distance of interest is ...

a = sin(A)·c/sin(C)

a = sin(32°)·(15 mi)/sin(85°) ≈ 7.979 mi

The fire is about 8 miles from tower B.

Fire towers A and B are located 15 miles apart. Rangers at fire tower A spot a fire at 32°, and rangers at fire tower B spot the same fire at 63º. How far from tower B is the fire to the nearest mile? A.7 B.8 C.9 D.5

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Fire towers A and B are located 15 miles apart. Rangers at fire tower A spot a fire at
32°, and rangers at fire tower B spot the same fire at 63º. How far from tower B is the
fire to the nearest mile?
A.7
B.8
C.9
D.5