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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.


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a

33+1 m

b

33-1 m

c

3-2 m

d

3-1 m 

answer is A.

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Detailed Solution

Let the river width be BD
Height of bridge=3 m So, CQ =3m
Question ImageHere, PQB =45 (angle of depression)
 RQD=30  (angle of depression)
 QC is height and  at BD
QCB=QCD=90
Now, in QBC,
tan30 =QCBC
13=3BC
BC=33)
Now, in QCD,
tan45=QCCD
1=3CD
CD=3
BD=BC+CD
=33+3
=3(3+1) )
Hence, width of river is 33+1.
Correct option is 1.
 
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