Cloud and Lake Reflection Proof

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Some Applications of Trigonometry

Cloud and Lake Reflection Proof

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 6

The problem

The angle of elevation of a cloud from a point hh metres above a lake is α,\alpha, and the angle of depression of its reflection in the lake is β.\beta. Prove that the height of the cloud above the lake is h(tan⁡β+tan⁡α)tan⁡β−tan⁡α.\dfrac{h(\tan\beta+\tan\alpha)}{\tan\beta-\tan\alpha}.

Step 1 · Your move

Let the cloud height above the water be HH. How far below the water surface is its optical reflection RR?

elevation α (cloud)depression β (reflection)hAFCMLR
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