Question

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

opposite sides of the river are 300 and 450

respectively. If the bridge is at a height of

2.5m from the river, find the width of the river​

Answer 1

Answer:

the angle of depression of the bank on opposite side of the river is 30° and 45° respectively. It is given that AC = 30 m.

Answer 2

Step-by-step explanation:

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)