33. A man sitting at a height of 20m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60{}^\circ and 30{}^\circ respectively. Find the width of the river.
33. A man sitting at a height of 20m on a tall tree on a small island in the middle of a river observes two poles directly opposite to each other on the two banks of the river and in line with foot of tree. If the angles of depression of the feet of the poles from a point at which the man is sitting on the tree on either side of the river are 60{}^\circ and 30{}^\circ respectively. Find the width of the river.

From the given information we can say that,

Assume width of river =PQ=(x+y)m

Height of tree will be (AB) =20m

Thus, in ΔABP

tan60{}^\circ=AB/ BP

\sqrt{3}=20/x

x=20\sqrt{3}m

In ΔABQ,

tan =AB/ BQ

1/\sqrt{3}=20/y

y=20\sqrt{3}

Then, (x+y)=20/\sqrt{3}+20\sqrt{3}

=\left[ 20+20(3) \right]/\sqrt{3}

=80\sqrt{3}

Hence, the width of the river is 80\sqrt{3}m