Towers A and B are located 10 miles apart. A ranger spots a fire at a 42-degree angle from tower A. Another fire ranger spots the same fire at a 64-degree angle from tower B. To the nearest tenth of a mile, how far from tower B is the fire?

Guest Feb 19, 2020

#1**+1 **

We can use the Law of Sines here

The remaining angle in the triangle (at the site of the fire) = 180 - 42 - 64 = 74°

Let D be the distance from tower B to the fire....so....we have

D / sin (42) = 10 / sin (74) rearrange as

D = 10* sin (42) / sin (74) ≈ 6.96 miles = 7 miles (to the nearest 10th )

CPhill Feb 19, 2020