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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
Options
\[3\sqrt{2}x\]
\[2\sqrt{3}x\]
\[\frac{\sqrt{3}}{2}x\]
\[\frac{2}{\sqrt{3}}x\]
Solution
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`
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