Question

the angle of elevation of a cloud from a point P which is h metres above the surface of the water in the lake is
$\alpha$ and the angle of depression of its image in the lake is theta prove that the height of the cloud above the surface of water is
$h \binom{ \tan(x) + \tan( \alpha ) }{ \tan(x) - \tan( \alpha ) }$
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Answer 1

Hey mate,

Question :-

The angle of elevation of a cloud from a point P which is h metres above the surface of the water in the lake is $\alpha$ and the angle of depression of its image in the lake is theta prove that the height of the cloud above the surface of water is

Answer :-

Let height of cloud from surface of lake be H.

$\frac{H-h}{AB}$ = tan θ

And $\frac{H+H}{AB}$ = tan θ

By addendo and dividendo, we get

$\frac{H-h+H+h}{H-h-H-h}$ = $\frac{tan θ+tan θ}{tan θ-tan θ}$

$\frac{2H}{-2h}$ = $\frac{tan θ+tan θ}{tan θ-tan θ}$

=> H = $h \binom{ \tan(x) + \tan( \alpha ) }{ \tan(x) - \tan( \alpha ) }$

Hope it helps...

$( Itz ❤Aakanksha❤ here! ) {}^{}$