SOLUTION: Fire station A and station B are 20 miles apart. They both respond to the same fire. Fire station A goes 40 degrees to reach the fire and station B goes 60 degrees to reach the f

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Question 260255: Fire station A and station B are 20 miles apart. They both respond to the same fire. Fire station A goes 40 degrees to reach the fire and station B goes 60 degrees to reach the fire. How far apart is station A from the fire?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Draw a triangle pointing up and label bottom left vertex A, bottom right vertex B and top vertex F.
put 20 as the distance between A and B. place a 40 in angle A and a 60 in angle B. Looking carefully at the picture, I see we can use law of sines to solve for AF.
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step 1 - set up the following low of sine proportion:
%2820%2Fsin%2880%29%29+=+%28AF%2Fsin%2860%29%29
step 2 - cross multiply to get
20%2Asin%2860%29+=+AF%2Asin%2880%29
step 3 - solve for AF in calculator ready form as
20%2Asin%2860%29%2Fsin%2880%29+=+AF
step 4 - estimate AF as
20%2A.866%2F.9848%29+=+AF
and then
AF+=+17.587
or about 17.6 miles