Question

A building is of unknown height. At a distance of 400 feet away from the building, an observer notices that the angle of elevation to the top of the building is 35º and that the angle of elevation to a poster on the side of the building is 15º. How far is the poster from the roof of the building? Round your answer to the nearest tenth.

Answer 1

Given :

A building is of unknown height. At a distance of 400 feet away from the building .

An observer notices that the angle of elevation to the top of the building is 35º and that the angle of elevation to a poster on the side of the building is 15º .

To Find :

How far is the poster from the roof of the building .

Solution :

Height is given by :

$h=d\times tan\theta$

( Here , $\theta$ is angle of elevation )

So , height of tower :

$H=400\times tan 35^o\\\\H=280.08 \ feet$

For height of poster :

$h=400\times tan 15^o\\\\h= 107.18\ feet$

Therefore , distance of poster from the roof of the building is :

$( 280.08-107.18) = 172.9\ feet$

Hence , this is the required solution .