Define the triangle components

Let $h_1$ be the standing part (perpendicular) and $h_2$ be the broken part (hypotenuse). The base is given as $12$ m.

$\text{Base} = 12, \quad \theta = 30°$

Calculate the standing part

Using $\tan(30°)$, we find the height of the standing part $h_1 = 12 \times \tan(30°)$.

$h_1 = 12 \times \frac{1}{\sqrt{3}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}$

Calculate the broken part

Using $\cos(30°)$, we find the length of the broken part $h_2 = \frac{12}{\cos(30°)}$.

$h_2 = \frac{12}{\sqrt{3}/2} = \frac{24}{\sqrt{3}} = 8\sqrt{3}$

Calculate total height

The original height of the tree is the sum of the standing part and the broken part.

$\text{Total Height} = h_1 + h_2 = 4\sqrt{3} + 8\sqrt{3} = 12\sqrt{3}$