Q. 143.8( 11 Votes )

The angle of elevation of a cloud from a point h metre above a lake is θ. The angle of depression of its reflection in the lake is 45°. The height of the cloud is
A. h tan (45° + θ)

B. h cot (45° – θ)

C. h tan (45° – θ)

D. h cot (45° + θ)

Answer :


Let A and B be the position of the cloud and its reflection in the lake.

Let the height of the cloud be H m.

Given EF = h m, ∠AED = θ and ∠DEB = 45°

As EF || CD

CD = h m

By law of reflection,

AC = BC = H

AD = AC – DC

= H – h

And,

BD = BC + DC

= H + h
In ΔDEB,


⇒ BD = DE
⇒ DE = H + h   ..... (1)
In ΔAED,


  ...... (2)
From (1) and (2),

⇒ H - h = (H + h) tan θ
⇒ H - h = H tan θ + h tan θ
⇒ H - H tan θ = h + h tan θ
⇒ H (1 - tan θ) = h (1 + tan θ)


As we know,

⇒ H = h (tan 45° + θ)

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