Question

It is found that on walking x meters towards a chimney in a horizontal line through its base, the elevation of its top changes from 30° to 60°. The height of the chimney is

पर्याय

• \[3\sqrt{2}x\]

• \[2\sqrt{3}x\]

• \[\frac{\sqrt{3}}{2}x\]

• \[\frac{2}{\sqrt{3}}x\]

Answer 1

Let h be the height of chimney AB 

Given that: angle of elevation changes from angle `∠D=30°`to .`∠C=60°`

Then Distance becomes `CD=x` and we assume `BC=y`

Here, we have to find the height of chimeny.

So we use trigonometric ratios.

In a triangle,ABC

`⇒ tan C=(AB)/(BC)` 

`⇒ tan 60°=(AB)/(BC)` 

`⇒ sqrt3=h/y`

`⇒y=h/sqrt3`

Again in a triangle ABD, 

`⇒ tan D=(AB)/(BC+CD)`

`⇒ tan 30°=h/(y+x)`

`⇒1/sqrt3=h/(y+x)` 

`⇒sqrt3h=y+x`

`⇒sqrt3h=h/sqrt3+x`                           `["put" y=h/sqrt3]`

`⇒ h(sqrt3-1/sqrt3)=x`

`⇒h=x/(sqrt3-1/sqrt3)`

`⇒h=(sqrt3x)/2`