A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60∘. when he moves 40m away from the bank, he finds the angle of elevation to be 30∘. Find the width of the river. (3 = 1.73)

Let the height of the tree = h and the width of the river =wThe angle of elevation when standing on the bank = 60∘When moved 40 m away from the bank, angle of elevation = 30∘Now, tan∠ of elevation = distanceheightNow, tan60=wh3=whh=w3 (1)Also, tan30=w+40h31=w+40hh=3w+40 (2)From (1) and (2)w3=3w+403w=w+40w=20 mThe width of the river is 20 m.

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

A person standing on the bank of a river observes that the ang

Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is $6 0^{\circ}$ . when he moves 40m away from the bank, he finds the angle of elevation to be $3 0^{\circ}$ . Find the width of the river. ( $3$ = 1.73)

None of these

Views: 988 students

Found 7 tutors discussing this question

Sophia Discussed

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is

6 0^{\circ}

. when he moves 40m away from the bank, he finds the angle of elevation to be

3 0^{\circ}

. Find the width of the river. (

3

= 1.73)

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Let the height of the tree =

h

and the width of the river =

w

The angle of elevation when standing on the bank =

6 0^{\circ}

When moved

40

m away from the bank, angle of elevation =

3 0^{\circ}

Now,

tan ∠

of elevation =

\frac{h e i g h t}{d i s t an ce}

Now,

tan 60 = \frac{h}{w}

3 = \frac{h}{w}

h = w 3

(1)

Also,

tan 30 = \frac{h}{w + 40}

\frac{1}{3} = \frac{h}{w + 40}

h = \frac{w + 40}{3}

(2)

From (1) and (2)

w 3 = \frac{w + 40}{3}

3 w = w + 40

w = 20

The width of the river is 20 m.

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

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	A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is $6 0^{\circ}$ . when he moves 40m away from the bank, he finds the angle of elevation to be $3 0^{\circ}$ . Find the width of the river. ( $3$ = 1.73)
Answer Type	Text solution:1
Upvotes	150

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60∘. when he moves 40m away from the bank, he finds the angle of elevation to be 30∘. Find the width of the river. (3​ = 1.73)

Text solutionVerified

Practice questions from similar books

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is $6 0^{\circ}$ . when he moves 40m away from the bank, he finds the angle of elevation to be $3 0^{\circ}$ . Find the width of the river. ( $3$ = 1.73)