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Towers A and B are located 10 miles apart. A ranger spots a fire at a 42-degree angle from tower A. Another fire ranger spots the same fire at a 64-degree angle from tower B. To the nearest tenth of a mile, how far from tower B is the fire?

 

 Feb 19, 2020
 #1
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We can use the Law of Sines here

 

The remaining angle in the triangle  (at the site of the fire) =   180 - 42  - 64  =  74°

 

Let D  be the distance  from tower B to  the fire....so....we  have

 

D / sin (42)  =  10 / sin (74)      rearrange as

 

D  =  10* sin (42) / sin (74)  ≈  6.96 miles  =  7 miles  (to the nearest  10th )

 

 

cool cool cool

 Feb 19, 2020

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