Question

If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower in the same straight line with it are complementary, find the height of the tower. 

 

Answer 1

Let AC be the height of tower is h meters. 

Given that: angle of elevation are  `∠B=90°-θ`and ` ∠D=θ`  and also`CD=4`m and`BC=9.m`.

Here we have to find height of tower.

So we use trigonometric ratios.

In a triangle, ADC

`tan θ=h/4` 

Again in a triangle ,ABC

⇒` tan (90°-θ)=AC/BC` 

⇒` cot θ=h/9` 

`⇒ 1/tanθ=h/9`  

put `tan θ=h/4` 

`⇒ 4/h=h/9` 

`⇒ h^2=36` 

`⇒ h=6`

Hence height of tower is 6 meters.