Question

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?

Answer 1

5 miles from the second tower 

Answer 2

Answer:5.455 miles

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
`(h)/(10-x)=tan34`

`(h)/(x)=tan39`

equating h values

10tan39=1.48429x

x=5.444 miles