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

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

Answer 2

5 miles from the second tower