Question

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

Answer 1

Answer:

it is the 12metres

Step-by-step explanation:

if the tree fall down =30 degrees angle

top and ground is 6m =6+6

=12m

Answer 2

In the figure,

Let AC be the initial height of the tree.

When the strom came, the tree broke from point B.

The broken part of the tree BC touches the ground at point D, making an angle 30° on the ground.

Also, given AD = 6m

In right angled ∆BAD,

$\sf tan(30°) = \dfrac{AB}{AD}$

$\implies \boxed{\bf AB = \dfrac{8}{\sqrt{3}}}$

Again, in ∆BAD,

$\sf cos(30°) = \dfrac{AD}{BD}$

$\implies \boxed{\bf BD = \dfrac{16}{\sqrt{3}}}$

$\sf ∴ AC = AB + BC$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: = AB + BD \: \: \: \: \: \: (∵ BC = BD)$

$\sf \: \: \: \: \: = \dfrac{8}{\sqrt{3}} + \dfrac{16}{\sqrt{3}} = 8\sqrt{3} \: m$

$\sf Hence \: the \: height \: of \: the \: tree \: is \: 8\sqrt{3} \: m$