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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?

Respuesta :

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[tex]=39^{\circ}[/tex]

second ranger indicated angle[tex]=34^{\circ}[/tex]

let x be the distance from second ranger to fire

thus [tex]\frac{h}{10-x}=tan34[/tex]

[tex]\frac{h}{x}=tan39[/tex]

equating h values

10tan39=1.48429x

x=5.444  miles

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