Applications of Trigonometric Functions

Question

A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is S 35 degrees W. How far is the first ranger from the fire?

Round to the nearest tenth of a mile

Answer 1

Draw a picture. If the bearing from the second ranger is 35°, then the line of sight angle from the horizon to the fire for the second ranger is 90°-35°=55°. So, tan55° = opposite/adjacent = x/9, where x is the distance from the first ranger to the fire.

x = 9 tan 55° miles