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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 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.

Answer:

**Solution:**

The term "angle of depression" refers to the angle produced between the horizontal line and the line of sight when an observer looks down at an object. It calculates the variation in our field of vision as we glance down.

From the given data, the fig. is made

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

Height of tree (AB) = 20 m

So, in ΔABP

tan 60^{o} = AB/ BP

√3 = 20/ x

x = 20/ √3 m

In ΔABQ,

tan 30^{o} = AB/ BQ

1/ √3 = 20/ y

y = 20√3

So, (x + y) = 20/ √3 + 20√3

= (20 + 20(3))/ √3

= 80/√3

**Therefore, the width of the river is 80/√3 m.**

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