Define Variables and Setup Triangle

Let the total height of the tree be $H = 24\text{ m}$. Let the tree break at height $h$ from the ground. The remaining part is of height $h$, and the fallen upper part forms the hypotenuse of a right-angled triangle with length $L = H - h$.

$H = h + L = 24$

Apply Trigonometric Ratio (Sine)

In the right-angled triangle formed with the ground, the angle $\theta = 30°$. The perpendicular is $h$ and the hypotenuse is $L$. Using $\sin 30° = \frac{\text{perpendicular}}{\text{hypotenuse}}$:

$\sin 30° = \frac{h}{L} = \frac{1}{2} \implies L = 2h$

Substitute and Solve for Height $h$

Substitute $L = 2h$ into the total height equation $H = h + L$:

$24 = h + 2h \implies 3h = 24 \implies h = \frac{24}{3} = 8\text{ m}$