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The angle of elevation of a cloud from a point $60 m$ above a lake is $30 °$ and the angle of depression of the reflection of the cloud in the lake is $60 ° .$ then the height of the cloud from the surface of the lake is

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60m

120m

160m

100m

answer is C.

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Detailed Solution

Given that the angle of elevation of a cloud from a point

60 m

above a lake is

30 °

and the angle of depression of the reflection of the cloud in the lake is

60 ° .

Consider the figure,
Question Image

We know,

tanθ = \frac{Perpendicular}{Base}

\tan 60 ° = \sqrt{3}

\tan 30 ° = \frac{1}{\sqrt{3}}

Δ PQC

\tan 30 ° = \frac{QC}{PQ}

tan 30 ° = x PQ ⇒ 13 = x PQ ⇒ PQ = x 3

Δ PQD

tan 60 ° = QD PQ ⇒ 3 = 120 + x x 3 ⇒ 2 x = 120 ⇒ x = 60 m

Then,

⇒ B C = x + 60 ⇒ B C = 60 + 60 ⇒ B C = 120 m

The height of the cloud from the surface of the lake is 120 m.
Therefore, option 3 is correct.

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