From a point P at height h above a still lake, the angle of elevation of a cloud is α and the angle of depression of its reflection in the lake is β. The height of the cloud above the lake is

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h(tan β + tan α)/(tan β − tan α). Let the cloud be H above the lake and d away. H − h = d tan α and H + h = d tan β (the reflection is H below the surface). Subtracting, d = 2h/(tan β − tan α), so H = h + d tan α = h(tan β + tan α)/(tan β − tan α).

From a point P at height h above a still lake, the angle of elevation of a cloud is α and the angle of depression of its reflection in the lake is β. The height of the cloud above the lake is

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