Book Online Demo

Check Your IQ

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 base of a cliff is circular. From the extremities of a diameter of the base, angles of elevation of the top of the cliff are $30^{\circ}$ and $60^{\circ}$ . If the height of the cliff be $500 m$ , then the diameter of the base of the cliff is

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

\frac{2000}{\sqrt{3}} m

\frac{1000}{\sqrt{3}} m

\frac{2000}{\sqrt{2}} m

1000 \sqrt{3} m

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

It is given that the angles of elevation of the top of the cliff are

30^{\circ}

and

60^{\circ}

The height of the cliff be

500 m

.
We have to find the diameter of the base of the cliff.
We use

tanθ = \frac{perpendicular}{base} .

△ AEC

\tan 60^{o} = \frac{500}{d_{1}}

\Rightarrow \sqrt{3} = \frac{500}{d_{1}}

[since

\tan 60^{o} = \sqrt{3}

]

\Rightarrow d_{1} = \frac{500}{\sqrt{3}} m

Similarly, in

△ BEC

\tan 30^{o} = \frac{500}{d_{2}}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{500}{d_{2}}

[since

\tan 30^{o} = \frac{1}{\sqrt{3}}

]

\Rightarrow d_{2} = 500 \sqrt{3} m

∴

Required diameter

= d_{1} + d_{2}

\Rightarrow diameter = \frac{500}{\sqrt{3}} + 500 \sqrt{3}

\Rightarrow diameter = \frac{2000}{\sqrt{3}} m

Thus, the diameter of the base of the cliff is

\frac{2000}{\sqrt{3}} m

.
Therefore, the correct option is 1.

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!