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?
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 )