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?.

Question

asked Aug 8, 2021 230k views

1 Answer

Boris Feld · Answer 1 · 2021-08-13T01:41:49+0000

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))

$Distance=692.82\ ft$