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The angle of elevation of a cloud from a point h mt above the surface of a lake is $θ$ and the angle of depression of its reflection in the lake is $φ$ . The height of the cloud is

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$\frac{h \sin (φ + θ)}{\sin (φ - θ)}$

$\frac{h \sin (φ - θ)}{\sin (φ + θ)}$

$\frac{h \sin (θ + φ)}{\sin (θ - φ)}$

$\frac{h \sin (θ - φ)}{\sin (θ + φ)}$

answer is A.

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Detailed Solution

$T a n θ = \frac{x}{y} T a n ϕ = \frac{2 h + x}{y} \Rightarrow x = \frac{2 h}{\cot θ . \tan ϕ - 1} C D = h + x = \frac{h \sin (ϕ + θ)}{\sin (ϕ - θ)}$

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