# 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.

### Mohammed

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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

Byju's Answer Standard X Mathematics

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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Calculating Heights and Distances

Standard X Mathematics

## 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 30Question ∘ and 45 ∘

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

**A**3(

3 −1) m

**B**3(

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 PAD ,

tan30= AD PD 3 1 = AD 3 AD=3 3

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).

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## 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)

Last updated at March 16, 2023 by Teachoo

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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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### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Guys, does anyone know the answer?