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?

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 =

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.

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

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