Question

The wind broke a 24 metres high tree. The top of this tree touches the ground. At what height did the tree break if the broken part makes an angle of 30° with the ground?​

Answer 1

Answer: The height above ground at which the tree broke is 8 meters.

Explanation:

Let the standing part of tree be of 'l' meters.

Therefore the broken part is of 24 - l meters.

By using trignometric functions

sin(30°) =
`(Perpendicular)/(Hypotenuse)`

`(1)/(2)`=
`(l)/(24-l)`

⇒ 2 × l = 24 - l

⇒3 × l = 24

⇒ l = 8

∴ The height above ground at which the tree broke is 8 meters.