Question

Atree breaks due to storm and the broken part bends so the top of the tree touches the ground making an angle of 30 degree with it the distance between them foot of the tree to the point where the top touches the ground is 8 M find the height of the tree

Answer 1

Let AD is the broken part of the tree.

So total length of the tree = AB + AD

Again AD = AC

So total length of the tree = AB + AC

Now in triangle ABC,

cos 30 = BC/AC

=> √3/2 = 8/AC

=> AC = 16/√3

Again tan 30 = AB/BC

 => 1/√3 = AB/8

=> AB = 8/√3

So height of tree = AB + AC

                         = 8/√3 + 16/√3

                         = 24/√3 m

Answer 2

Let, the height of the tree be H
given, angle= 30°
distance between the top of tree and ground= 8m
thus, it makes a triangle
height of the tree now= perpendicular
height of broken part= hypotenuse
base= 8m
perpendicular/base= tan30° = √3
or, p/8= √3
or, p= 8√3
thus, h= √{(8√3)²+(8)²}
thus total height of the tree= h+p as the broken part is included with the perpendicular