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 isA. h tan (45° + θ)B. h cot (45° – θ)C. h tan (45° – θ)D. h cot (45° + θ)

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)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trick to learn all Trigonometric Formulae28 mins
Champ Quiz | Trigger on Trigonometry47 mins
Fundas of Trigonometry50 mins
Champ Quiz | Trigonometry Important Questions33 mins
NCERT | Trigonometric Identities52 mins
Champ Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFREE Class
NCERT | Imp. Qs. on Trigonometry42 mins
Quiz | Trail of Mixed Questions on Trigonometry59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses