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Two fire rangers in watch towers that are 10 miles apart spotted a fire at the same time. The first ranger indicated that the position of the fire made an angle of 39° with the line between the towers. The second ranger indicated that it made an angle of 34° with the same line. How far is the second tower from the fire?

Verified Answer :

mommyamber40

5 miles from the second tower

Answer:5.455 miles

Step-by-step explanation:

Suppose the height of watch towers are same(h)

and distance between them is 10 miles

first ranger indicated angle\(=39^{\circ}\)

second ranger indicated angle\(=34^{\circ}\)

let x be the distance from second ranger to fire

thus \(\frac{h}{10-x}=tan34\)

\(\frac{h}{x}=tan39\)

equating h values

10tan39=1.48429x

x=5.444  miles

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