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Question

# 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 cloud in the lake is 60∘. Find the height of the cloud.

A

820 metres

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B

120 metres

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C

190 metres

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D

320 metres.

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Solution

## The correct option is B 120 metres Concept: 2 Marks Application: 2 Marks Let AB be the surface of the lake and let P be a point vertically above A such that AP = 60 m Let C be the position of the cloud and let D be its reflection in the lake. Draw PQ⊥CD, Then, ∠QPC=30∘,∠QPD=60∘, BQ = AP = 60 m Let CQ=x metres. Then, BD=BC=(x+60) m From right ΔPQC, we have PQCQ=cot30∘=√3 ⇒PQx m=√3⇒PQ=x√3 m From right ΔPQD, we have PQQD=cot60∘=1√3 ⇒PQ(x+60+60)m=1√3⇒PQ=(x+120)√3 m Equating the values of PQ from (i) and (ii), we get x√3=(x+120)√3 m ⇒3x=x+120⇒2x=120⇒x=60 ∴ height of the cloud from the surface of the lake =BC=(60+x)m=(60+60) m=120 m Hence, the height of the cloud from the surface of the lake is 120 metres.

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