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If the angle of elevation of a cloud from a point h meters abo

Question

If the angle of elevation of a cloud from a point $h$ meters above a lake is $α$ and the angle of depression of its reflection in the lake be $β$ , prove that the distance of the cloud from the point of observation is $\frac{2 h tan α}{tan β - tan α}$ .

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If the angle of elevation of a cloud from a point

h

meters above a lake is

α

and the angle of depression of its reflection in the lake be

β

, prove that the distance of the cloud from the point of observation is

\frac{2 h tan α}{tan β - tan α}

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11 mins ago

Text solutionVerified

Let

OB = x

Now

tan α = \frac{γ}{x}

________ (1)

tan β = \frac{h + h + y}{x}

∴ tan β = \frac{2 h + y}{x}

_______ (2)

∴ \frac{tan α}{tan β} = \frac{γ}{2 h + y}

∴ 2 h tan α + y tan α = γ tan β

∴ 2 h tan α = γ (tan β - tan α)

∴ γ = \frac{2 h tan α}{tan β - tan α}

Hence proved.

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Question Text	If the angle of elevation of a cloud from a point $h$ meters above a lake is $α$ and the angle of depression of its reflection in the lake be $β$ , prove that the distance of the cloud from the point of observation is $\frac{2 h tan α}{tan β - tan α}$ .
Answer Type	Text solution:1
Upvotes	150