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?

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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