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A cloud is observed from a point that is m metres above the surface of a lake. If the angle of elevation to the cloud is α and the angle of depression to its image in the water is β, then the cloud’s height is

1. a sin(α + β) metre / sin(α − β)
2. a sin(α + β) metre / sin(β − α)
3. a sin(α − β) metre / sin(α + β)
4. None of these

Correct answer: a sin(α + β) metre / sin(β − α)

Solution

The correct option is derived from the relationship between the angles of elevation and depression, which involves trigonometric functions. The height of the cloud can be expressed using the sine of the angles, leading to the formula that incorporates both angles in the correct manner.

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