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Two​ fire-lookout stations are 190 miles ​apart, with station A directly south of station B. Both stations spot a fire. The bearing of the fire from station A is Upper N 55 degrees Upper E and the bearing of the fire from station B is Upper S 60 degrees E. How​ far, to the nearest tenth of a​ mile, is the fire from each lookout​ station?

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MathPhys

Step-by-step explanation:

Let's say the position of the fire is point C.

Bearings are measured from the north-south line.  So ∠BAC = 55°, and ∠ABC = 60°.

Since angles of a triangle add up to 180°, ∠ACB = 65°.

Using law of sine:

190 / sin 65° = a / sin 60° = b / sin 55°

Solving:

a = 181.6

b = 171.7

Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.

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