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(B) Let $h$ be the height of the cloud above the surface of the lake. The point $P$ is $25 \, m$ above the lake surface.Let $x$ be the height of the c

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(B) Let $h$ be the height of the cloud above the surface of the lake. The point $P$ is $25 \, m$ above the lake surface.Let $x$ be the height of the cloud above the level of point $P$,so $h = x + 25$.The distance of the reflection of the cloud below the surface is $h = x + 25$.The total vertical distance from $P$ to the reflection is $(x + 25) + 25 = x + 50$.Let $y$ be the horizontal distance from $P$ to the vertical line of the cloud.From the angle of elevation: $	an(30^o) = \frac{x}{y} \Rightarrow y = \frac{x}{	an(30^o)} = x\sqrt{3}$.From the angle of depression: $	an(60^o) = \frac{x + 50}{y} \Rightarrow y = \frac{x + 50}{\sqrt{3}}$.Equating the two expressions for $y$: $x\sqrt{3} = \frac{x + 50}{\sqrt{3}}$.$3x = x + 50$ $\Rightarrow 2x = 50$ $\Rightarrow x = 25 \, m$.The total height of the cloud from the surface is $h = x + 25 = 25 + 25 = 50 \, m$.

If the angle of elevation of a cloud from a point $P$ which is $25 \, m$ above a lake is $30^o$ and the angle of depression of the reflection of the cloud in the lake from $P$ is $60^o$,then the height of the cloud (in meters) from the surface of the lake is:

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