Question

A forest ranger sights a fire directly to the south. A second ranger, 10 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is S 35° W. How far is the first ranger from the fire?

Answer 1

The problem can be depicted in figure as:

The first ranger sight fire to south from A to C

The second ranger sights fire at east of first ranger at a distance 10 miles

Thus,

$_{\angle SBC=35^o}$

Thus,

$\angle ABC=90^o-35^o=55^o$

In triangle ABC,

$\text{tan}55^o=\frac{AC}{AB}$$1.42=\frac{AC}{10}$$AC=14.2\text{miles}$

So the first ranger is at a distance 14.2 miles from the fire.