A forest ranger sights a fire directly to the south. A second ranger, 7 miles east of the first ranger, also sights the fire.

Question

3 years ago

14

The bearing from the second ranger to the fire is Upper S 22 degrees Upper W. How far is the first ranger from the fire?

1 answer:

tresset_1 [31] · Answer 1 · 2022-01-11T23:09:56+03:00

Answer:

17 miles

Step-by-step explanation:

Let the first Ranger be at A and the second Ranger at Point B.

Using alternate angles, ∠AXB=22°.

We want to determine the distance of the first ranger at point A to the fire(X).

Using trigonometry,

Tan = Opposite/Adjacent

Tan 22°= 7/|AX|

|AX| X Tan 22°= 7

|AX| = 7/Tan 22°=17.32560797391

= 17 miles( to the nearest mile)

The first ranger is 17 miles from the fire.

A forest ranger sights a fire directly to the south. A second​ ranger, 7 miles east of the first​ ranger, also sights the fire.