Question

31. From a point on a bridge across a river the angles of depression of the banks on opposite
side of the river are 30° and 45° respectively. If bridge is at the height of
30 m from the banks, find the width of the ​

Answer 1

Answer:

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 =300,450

So,∠QPA=300

 ∠RPB=450

We need to find AB=?

 

Since , PD height so it will be perpendicular at AB

 

∠PDA=∠PDB=900

And line QR is parallel to line AB

  ∠PAD=∠QPA=300   (Alternate angle)

Similarly,

∠QPB=∠PBD=450          (Alternate angle)

 

Now, in triangle PAD ,

  tan30=ADPD

 31=AD3

 AD=33

Now in triangle PBD ,

   tan450=DBPD

 1=DB3

 DB=3

AB=AD+DB

  =33+3

 =3(3+1)

Hence width of river is 3(3+1).