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

Answer:

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

Step-by-step 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.

$tan 29\°= \frac{AC}{AB}\\\\tan 29\° = \frac{x}{99}\\\\x= 99\times tan29\°\\\\x \approx 54.88\ mi$

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