Question

The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is ____________.

विकल्प

• `10 sqrt3` m

• `5 sqrt3` m

• `sqrt3` m

• `sqrt3//5` m

Answer 1

The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is `underline(5 sqrt3  "m")`.

Explanation:

Let BD be the height of the tree and C be the breaking point.

In rt `angle"ABC, tan"  30^circ = "BC"/"AB" => 1/sqrt3 = "BC"/5`

`=> "BC" = 5/sqrt3`

Also cos `30^circ = "AB"/"AC"`

`=> sqrt3/2 = 5/"AC"`

`=> "AC" = 10/sqrt3`

`therefore` Height of the tree = BC + AC

= `5/sqrt3 + 10/sqrt3 = 15/sqrt3`

`= 15/sqrt3 xx sqrt3/sqrt3`

`= (15 sqrt3)/3`

`= 5 sqrt3  "m"`