Question

12. A tree is broken by the storm. The top of the tree touches the ground making an angle 30° and at a distance of 30 m from the root. Find the height of the tree?​

Answer 1

ANSWER

Segment AB represents the height of the tree.

The tree breaks at point D.

∴ Segment AD is the broken part of tree which then takes the position of DC.

∴AD=DC

Given m∠DCB=30

∘

,BC=30m

In right angled ΔDBC,

tan30

∘

=

BC

BD

⇒

3

1

=

30

BD

⇒BD=

3

30

∴BD=10

3

m

Also cos30

∘

=

DC

BC

⇒

2

3

=

DC

30

⇒DC=

3

60

∴DC=20

3

m

Hence AD=DC=20

3

m

From the figure, AB=AD+DB

∴AB=20

3

+10

3

⇒AB=30

3

m

∴AB=30×1.73

∴AB=51.9m

Hence, the height of tree is 51.9m