Question

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 1

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,

⇒ 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)