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At a point A, 20 m above the level of water in a lake, the angle of elevation of a cloud is $30 °$ . The angle of depression of the reflection of the cloud in the lake, at A, is $60 °$ . Find the distance of the cloud from A.

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40 m

10 m

20 m

30 m

answer is D.

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Detailed Solution

Given that at a point A. 20 meters above the level of water in a lake. the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at is

A

60 °

We have to find the distance of the cloud from A.
Question Image

right-angle triangle, tan θ = Opposite side Hypotenuse

From,

Δ A B C

h x = tan30 ° = 13 ⇒ x = 3 h .

From

Δ A B D

Hence distance of the cloud = 40 m
The height of the cloud from the surface is 40 m.
Therefore, the correct option is 4.

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