Two fire-lookout stations are 270 miles apart, with station. A directly south of

Question

Two fire-lookout stations are 270 miles apart, with station. A directly south of station B. Both stations spot a fire The bearing of the fire from station A is N55 degree E and the bearing of the Fire from station B is S60 degree E How far to the nearest tenth of a mile, is the fire from each lookout station? The distance from station B to the fire is miles (Round to the nearest tenth.) The distance from station A to the fire is miles. (Round to the nearest tenth.) Enter your answer in each of the answer boxes.

Explanation / Answer

Remaining angle of the triangle=180-55-60=65°

sin 65/270=sin55/x

x=270sin55/sin65=244 miles

Therefore distance from station B=244miles

sin65/270=sin 60/y

y=270sin60/sin65=258miles

Therefore distance from station A=258miles

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