Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making 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 10 meters. Find the height of the tree.

Answer 1

Let AC be the height of the tree which is (x + h) m

Given, the broken portion of the tree is making an angle of 30^o with the ground.

From the fig.

In ΔBCD, we have

tan 30^o = BC/ DC

1/√3 = h/ 10

h = 10/ √3

Next, in ΔBCD

cos 30^o = DC/BD

√3/2 = 10/x

x = 20/√3 m

So,

x + h = 20/√3 + 10/√3

= 30/√3

= 10√3 = 10(1.732) = 17.32

Therefore, the height of the tree is 17.32 m