Question

Question 8
If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Answer 1

The statement is false.
We know that, if P is a point above the lake at a distance "d", then the reflection of the point in the lake would be at the same distance "d". Also, the angle of elevation and depression from the surface of the lake is same.

Here, the man is standing on a platform 3m above the surface, so its angle of elevation to the cloud and angle of depression to the reflection of the cloud is not same.

Another method-

From the figure-

Let, $PM=y$

$CM=OC=h$

$\tan {\theta }_1=\frac{h-3}{y}\Rightarrow y=\frac{x-3}{\tan {\theta }_1}...\left(i\right)$

And,

$\tan {\theta }_2=\frac{x+3}{y}\Rightarrow y=\frac{x+3}{\tan {\theta }_2}....\left(ii\right)$

From (i) and (ii)

$\frac{x-3}{\tan {\theta }_1}=\frac{x+3}{\tan {\theta }_2}\Rightarrow \tan {\theta }_1=\frac{x-3}{x+3}\tan {\theta }_2\because \frac{x-3}{x+3}=1\Rightarrow x-3=x+3$

Which is not possible.

Hence, given statement is fales.