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.
The distance from the fire to the first ranger is 17 miles
Since A forest ranger sights a fire directly to the south. A second ranger, 7 miles east of the first ranger, also sights the fire.
Let us assume the first Ranger be at A and the second Ranger at Point B.
Now here we used alternate angles, ∠AXB=22°.
Now
Using trigonometry,
[tex]Tan = Opposite\div Adjacent\\\\Tan = 7\div |AX|\\\\|AX| = 7\div Tan 22[/tex]
= 17 miles
Hence, we can conclude that The distance from the fire to the first ranger is 17 miles
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