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# from a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 respectively. if the bridge is at a height of 3 m from the banks, then find the width of the river.

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### Mohammed

Guys, does anyone know the answer?

get from a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 respectively. if the bridge is at a height of 3 m from the banks, then find the width of the river. from screen.

## From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30∘ and 45∘ respectively. If the bridge is at a height of 6 m from the banks find the width of the river.A. 6 mB. 6 √3 mC. 3 √3 mD. 6+6 √3 m

From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30∘ and 45∘ respectively. If the bridge is at a height of 6 m from the banks find the width of the river.A. 6 mB. 6 √3 mC. 3 √3 mD. 6+6 √3 m Calculating Heights and Distances

From a point ... Question

From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are

30 ∘ and 45 ∘

respectively. If the bridge is at a height of 6 m from the banks find the width of the river.

A 6 m B 6√3 m C 3√3 m D 6+ 6√3 m Open in App Solution

The correct option is D

6+ 6√3 m If the line through P is the bridge

In Δ PDA, ∠ A = 30 ∘ PD = 6 AD = PD √ 3 = 6 √ 3 In Δ PDB, ∠ B = 45 ∘ DB = PD = 6

Hence width of the river = 6 + 6

√ 3 = 6(1+ √ 3 ) m Suggest Corrections 30 SIMILAR QUESTIONS

Q. From the point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are

30 ∘ and 45 ∘

, respectively. If the bridge is at a height of

3 m

from the banks, find the width of the river.

Q. From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are 30

o and 45 o

respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.

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स्रोत : byjus.com

## From the point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are 30^∘ and 45^∘ , respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

Click here👆to get an answer to your question ✍️ From the point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are 30^∘ and 45^∘ , respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. From the point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are 30

Question ∘ and 45 ∘

, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.

A3(

3 ​ −1) m

B3(

3 ​ +1) m

C(3+

3 ​ ) m

D(3−

3 ​ ) m Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Let width of river =AB

And bridge is at height of  3m from banks

So, DP=3m

Angel of depression of banks on the opposite sides of river are =30

0 ,45 0 So,∠QPA=30 0 ∠RPB=45 0

We need to find AB=?

Since , PD height so it will be perpendicular at AB

∠PDA=∠PDB=90 0

And line QR is parallel to line AB

∠PAD=∠QPA=30 0 (Alternate angle) Similarly, ∠QPB=∠PBD=45 0 (Alternate angle)

Now in triangle PBD ,

tan45 0 = DB PD ​ 1= DB 3 ​ DB=3 AB=AD+DB =3 3 ​ +3 =3( 3 ​ +1)

Hence width of river is 3(

3 ​ +1). Solve any question of Some Applications of Trigonometry with:-

Patterns of problems

>

243 127

स्रोत : www.toppr.com

## Example 7

Example 7 From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 , respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. Let the width of the river = AB And the bridge is at a Check sibling questions

## Example 7 - Chapter 9 Class 10 Some Applications of Trigonometry (Term 2)

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### Transcript

Example 7 From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 and 45 , respectively. If the bridge is at a height of 3 m from the banks, find the width of the river. Let the width of the river = AB And the bridge is at a height of 3m from the banks, So, DP = 3 metre Angle of depression of the banks on opposite sides of the river are 30 and 45 respectively. So, QPA = 30 and RPB = 45 We need to find width of river i.e. AB Since PD is the height, it is perpendicular to AB PDA = PDB = 90 Lines PQ & AB are parallel, And AP is the transversal PAD = QPA PAD = 30 Similarly, Lines PR & AB are parallel, And BP is the transversal PBD = RPB PBD = 45 Now, AB = AD + BD = 3 3 + 3 = 3( 3 + 1) Width of the river = AB = 3( 3 + 1) metre

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