Question

at a point 20m above the level of water of a lake, the angle of elevation of a cloud is 30° The angle ofdepression of the reflection of the cloud in the lake is 60° Find the height of cloud above
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Answer 1

SOLUTION:-

Given:

At a point 20m above the level of water of a lake, the angle of elevation of a cloud is 30°.

The angle of depression of the reflection of the cloud in the lake is 60°.

To find:

The height of the cloud.

Explanation:

Let BE be the surface of the lake. Suppose C be the position of the cloud & C be its reflection in the lake.

Then, AB = 20m.

•Assume CD= R m

•CE= C'E = (R +20)m

In ∆ACD,

tan30° = CD/AD

=) 1/√3 = R/AD

=) AD= R√3...............(1)

&

sin30° = CD/AC

=) 1/2 = R/AC

=) AC= 2R...................(2)

In ∆ADC',

tan60° = C'D/AD

=) √3 = (R+20)+20/AD

=) AD= (R+40)/√3.............(3)

From equation (2)& (3), we get;

=) R√3 = (R+40)/√3

=) 3R = R +40

=) 3R -R =40

=) 2R = 40

=) R= 40/2

=) R= 20m

Thus,

The height of the cloud is 20m.

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Answer 2

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