(Q9) A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground by making 30o angle with the ground. The distance between the foot of the tree and the top of the tree on the ground is 6 m. Find the height of the tree before falling down.

Solution :

oh6m30x

Distance between the foot of tree and the point of contact of the top of the tree on the ground = 6 cm.

Let the length of the remaining part be = h m.

Let the length of the broken part be = x m.

Angle made by the broken part with the ground = 30o.

From the figure

tan ° =
h
1
√
 =
h

∴ h =
√
 =
× 2
√
 = 2√ m
Also cos ° =
x
√
 =
x
x =
√
 =
4 ×
√
 = 4√

∴ Height of the tree = broken part + remaining part

= x + h = 2√ + 4√ = 6√ m