From a point 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 5m from the banks, find the width of river
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Answer:
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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