Get 2 FREE Instant-Explanations on Filo with code FILOAPP

The angle of elevation of a stationary cloud from a point 2500

Question

The angle of elevation of a stationary cloud from a point $2500$ m above a lake is $1 5^{0}$ and from the same point the angle of depression of its reflection in the lake is $4 5^{o}$ . The height (in meters) of the cloud above the lake, given that $cot 1 5^{o} = 2 + 3$ , is

2500

25002

25003

5000

Views: 1,023 students

Found 5 tutors discussing this question

Ava Discussed

The angle of elevation of a stationary cloud from a point

2500

m above a lake is

1 5^{0}

and from the same point the angle of depression of its reflection in the lake is

4 5^{o}

. The height (in meters) of the cloud above the lake, given that

cot 1 5^{o} = 2 + 3

, is

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Let

EB = x

m, then

tan 1 5^{0} = \frac{h}{x}

\Rightarrow x = h cot 1 5^{0}

...(1)

and from triangle EBD, we can get

tan 4 5^{o} = \frac{h + 5000}{x}

\to x \cdot 1 = h + 5000

...(2)

From (1) and (2)

\Rightarrow h cot 1 5^{0} = h + 5000

\Rightarrow h (2 + 3) = h + 5000

\Rightarrow h = \frac{5000}{3 + 1} = \frac{5000 ( 3 - 1 )}{3 - 1} = 2500 (3 - 1) m

∴

height of cloud is

2500 + 2500 (3 - 1)

= 25003

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	The angle of elevation of a stationary cloud from a point $2500$ m above a lake is $1 5^{0}$ and from the same point the angle of depression of its reflection in the lake is $4 5^{o}$ . The height (in meters) of the cloud above the lake, given that $cot 1 5^{o} = 2 + 3$ , is
Answer Type	Text solution:1
Upvotes	150