AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The angle of elevation of a cloud from a point 100 meter above the surface of a lake is $30 °$ and the angle of depression of its image in the lake is $60 °$ then height of the cloud above the lake is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

100 m

50 m

200 m

150 m

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is given that the angle of elevation of a cloud from a point 30

°

and is 100 meter above the surface of a lake. The angle of depression of its image in the lake is

60 °

.
According to the given data the figure has been drawn below.
Question Image

Δ A B C,

tan θ = P e r p e n d i c u l a r b a s e

tan 30 ° = A C B C

\tan 30 ° = \frac{h - 100}{d}

\frac{h - 100}{d} = \frac{1}{\sqrt{3}}

(\tan 30 ° = \frac{1}{\sqrt{3}})

.....(1)
In

Δ B C D,

tan θ = P e r p e n d i c u l a r b a s e

tan 60 ° = C D B C

\tan 60 ° = \frac{h + 100}{d}

\frac{h + 100}{d} = \sqrt{3}

(\tan 60 ° = \sqrt{3})

...........(2)
Dividing equation (1) by (2) , we get

\frac{h - 100}{h + 100} = \frac{1}{3}

\Rightarrow 3 h - 300 = h + 100

\Rightarrow 3 h - h = 300 + 100

\Rightarrow 2 h = 400

\Rightarrow h = 200

∴

Height above the lake is 200 m.
So the correct option is 3.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!