Question

while hiking you see a 100ft observation tower on top of a 1100ft hill. The angle of elevation to the top of the tower is 6. How far away is the tower?.​

Answer 1

Answer:692.82 ft

Explanation:

Given

Height of tower is
`h=100\ ft`

Tower is mounted at the top of
`H=1100\ ft` hill

angle of elevation
`\theta =60^(\circ)`

Using figure we can write

`\tan \theta =\frac{h+H}{\text{Distance}}`

`\tan 60^(\circ)=\frac{100+1100}{\text{Distance}}`

`Distance =(1200)/(\tan 60^(\circ))`

`Distance=(1200)/(√(3))`

`Distance=692.82\ ft`