In the Adirondack Mountains near Tupper Lake, New York, forest fire observers used fire observation towers for over 70 years. The people who staffed the towers reported forest fires and smoke sightings. As many as 57 towers were used by the observers; however, in the early 1980s, the State of New York determined that the towers were no longer needed since aerial observations had become commonplace.

Question

Suppose a forest ranger in one of the observation towers in the Adirondacks sights a fire 32° east of north while a ranger in a tower 13 miles due east of the first ranger sights the same fire at 49° west of north. How far is the fire from each ranger? (Round your answers to two decimal places.)

Answer 1

the base of the triangle is the east-west line between the rangers

the angle at the 1st ranger is ... 90º - 32º

the angle at the 2nd ranger is ... 90º - 49º

the 3rd angle is between the ranger stations (from the fire)
... this distance is 13 mi

use the law of sines to find the other two distances (rangers to fire)