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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?

A forest ranger sights a fire directly to the south. A second ranger, 10 miles east-example-1
User Raj Damani
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6.5k points

1 Answer

4 votes

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=(AC)/(AB)
1.42=(AC)/(10)
AC=14.2\text{miles}

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

A forest ranger sights a fire directly to the south. A second ranger, 10 miles east-example-1
User Cyonder
by
6.4k points
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