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

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13 Mar 2019 Width of River

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 60° and 45° respectively. If the bridge is at a height of 9 meter from the banks then find the width of the river? Assume both the banks are at same ground level.

OPtion

1) 14.02 m
2) 14.11 m
3) 14.20 m
4) 14.40 m
5) 14.73 m
6) 14.35 m
7) 14.05 m
8) 14.53 m
9) 14.63 m
10) None of these

Solution

Let A and B be the two sides of the river and C be the point on the bridge. D is a point on straight line between A and B such that CD = 9 meters

Width of the river would = AD+BD

In right angled triangle ACD,
tan 60° = CD/AD
=> √3 = 9/AD
=> AD = 9/√3 = 3√3

In right angled triangle BCD,
tan 45° = CD/BD
=> 1 = CD/BD
=> CD = BD = 9 meters

So the width of the river is AD+BD = 9+3√3 = ~14.20 meters

Correct Option: 3 Best Solution (5)

G.S.Kantharao   5 years AGO

Distance between the banks =9+3√3=14.20.
So the right option is 3👈

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SAYAN CHATTERJEE   5 years AGO

Width of the river is 9*(1/tan 45+1/tan60)
= 14.20
Option 3.

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kavya mv   5 years AGO

tan 60=9/adj=5.2
tan45=9/adj=9
width of river =9+5.2=14.2

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Manuja S   5 years AGO

tan60=9/adj
adj=5.2
tan45=9/adj1
adj1=9
then width=adj+adj1=14.20

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indu m j   5 years AGO

tan 60=9/adj =5.2
tan 45=9/adj=9
by adding these two we wll get width of tiver

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