A man sitting at a height of 20 m 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 the 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° and 30° respectively. Find the width of the river.

A man sitting at a height of 20 m 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 the 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° and 30° respectively. Find the width of the river.

Let width of the river be DC= DB+BC ⇒ ) m.

In ∆ABC

tan 60° =

20 = √3

-----(1)

Now in ∆ABD

tan 30° =

Therefore width of river = ) m.

⇒

⇒ ⇒ ⇒ m.

Width of river is m.

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