Question

A forest ranger sights a fire directly to the south. A second​ ranger, 99 miles east of the first​ ranger, also sights the fire. The bearing from the second ranger to the fire is Upper S 29 degrees Upper WS 29° W. How far is the first ranger from the​ fire?

Answer 1

The first ranger is approximately 54.88 miles away from the fire.

Explanation:

We have drawn the diagram for your reference.

Given:

Distance between first ranger and second ranger (AB)= 99 miles

Angle between fire and second ranger
`\angle B` =
`29\°`

We need to find the distance between the first ranger from the​ fire.

Solution:

Let the distance between the first ranger from the​ fire (AC) be 'x'.

So we can say that;

We know that;

tan of angle B is equal to opposite side divided by adjacent side.

`tan 29\°= (AC)/(AB)\\\\tan 29\° = (x)/(99)\\\\x= 99* tan29\°\\\\x \approx 54.88\ mi`

Hence the first ranger is approximately 54.88 miles away from the fire.