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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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 are30 ∘ 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 30o 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.
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 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
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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Guys, does anyone know the answer?