Question

At a point A, 20 metres 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.

Answer 1

I hope you find your answer

Answer 2

Answer:

Refer to the attachment for diagram !

Here,

• EC = h
• DC = 20
• ED = h - 20
• FD = h + 20

Correction to be noted in the diagram

Consider Δ AED

Here, Tan 30 = Opposite / Adjacent

=> Tan 30 = h - 20 / AD

=> 1 / √3 = h - 20 / AD

=> AD = ( h - 20 ) √3

Now consider Δ AFD

=>  Tan 60 = Opposite / Adjacent

=> √3 = DF / AD

=> √3 = ( h + 20 ) / √3 ( h - 20 )

Taking the denominator that side we get,

=> √3 ( h - 20 ) × √3 = h + 20

=> 3 ( h - 20 ) = h + 20

=> 3h - 60 = h + 20

=> 3h - h = 20 + 60

=> 2h = 80

=> h = 40

Hence the height of the cloud from ground is 40m.

So, from A it is simple to calculate.

In Δ AED, Sin 30 = DE / AE

=> 1 / 2 = ( h - 20 ) / ( AE )

Substituting h = 40, we get,

=> 1 / 2 = ( 40 - 20 ) / AE

=> 1 / 2 = 20 / AE

=> AE = 20 × 2 = 40 m

Hence the distance of cloud from A is 40m.

Note: Corrections in the diagram are mentioned in the start.