Question

A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

Answer 1

suppose height=h
tan(A)= (24-h)/h
1/√3=(24-h)/h
h(1+√3)=24√3
h=24√3/(1+√3)

Answer 2

Answer:

Height of the tree from where it break is 8 cm.

Step-by-step explanation:

Given: Original Height of the tree = 24 cm

           Angle made by top of tree with the ground = 30°

To find: Height from where tree is break.

Let x be the Height from where tree broke.

height of tree that falls to ground = 24 - x

Figure is attached.

In ΔABC,

using trigonometric ratio, we get

$sin\,30^{\circ}=\frac{AB}{AC}$

$\frac{1}{2}=\frac{x}{24-x}$

24 - x = 2x

2x + x = 24

3x = 24

x = 8

Therefore, Height of the tree from where it break is 8 cm.