Question

If the angles of elevation of the top of a tower from two points distant a and b from the  base and in the same straight line with it are complementary, then the height of the tower is 

Options

•  ab

• \[\sqrt{ab}\]

• \[\frac{a}{b}\]

• \[\sqrt{\frac{a}{b}}\]

Answer 1

Let h be the height of tower AB_. 

Given that: angle of elevation of top of the tower are `∠D=θ`and .`∠C=90°-θ`

Distance`BC=b` and `BD=a`

Here, we have to find the height of tower.

So we use trigonometric ratios.

In a triangle, ABC

`tan D=(AB)/(BC)`  

`⇒ tan (90°-θ)=h/b`

`⇒ cotθ=h/b` 

Again in a triangle ABD, 

`tan D=(AB)/(BD)` 

`⇒ tan θ=h/a` 

`⇒1/cot θ=h/a` 

⇒ `b/h=h/a` 

`⇒h^2=ab`

`⇒ h=sqrt(ab)`

Put `cotθ=h/b `