The angle of elevation of a cloud from a point 100 m above a lake is 30 degree and the angle of depression of its reflection in the lake is 60 degree. What will be the height of the cloud?

The angle of elevation of a cloud from a point 100 m above a lake is 30 degree and the angle of depression of its reflection in the lake is 60 degree. What will be the height of the cloud? Correct Answer 100 m

Let the height of the cloud be h m and base distance be b m. ➩ tan 30 = height / base distance ➩ 1 / √3 = h / b ➩ b = h√3 According to the questio➩ tan 60 = height / base distance ➩ √3 = (h + 100 + 100) / b Substituting the value of b in terms of h from the above equation ➩ √3 = (h + 200) / h√3 ➩ 3h = h + 200 ➩ 2h = 200 ➩ h = 100 m
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