A tree breaks due to storm. The broken part makes an angle of 30 degrees with the ground and the distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the total

Let $h$ be the height of the standing part of the tree and $L$ be the length of the broken part that touches the ground. The total height of the tree is $H = h + L$.
The distance from the foot of the tree to where the top touches the ground is $8 \text{ m}$.
The angle made by the broken part with the ground is $30^\circ$.

We use the tangent function, which relates the opposite side ($h$) to the adjacent side ($8 \text{ m}$).

We know that $\tan(30^\circ) = \frac{1}{\sqrt{3}}$.

We use the cosine function, which relates the adjacent side ($8 \text{ m}$) to the hypotenuse ($L$).

We know that $\cos(30^\circ) = \frac{\sqrt{3}}{2}$.

The total height is the sum of the standing part and the broken part.

To rationalize the denominator, multiply the numerator and denominator by $\sqrt{3}$:

The height of the tree is $8\sqrt{3} \text{ m}$.