Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is ______.

Options

• 60 m

• 30 m

• 40 m

• 20 m

Answer 1

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is 20 m.

Explanation:

In right ΔQTR

tan 60° = `y/x` `\implies` y = `sqrt(3)x`  ....(i)

In right ΔPTR

tan 30° = `y/(x + 40) \implies` y = `(x + 40)/sqrt(3)`  ....(ii)

From (i) and (ii),

`sqrt(3)x = (x + 40)/sqrt(3)`

`\implies` x = 20m