1. **State the problem:** We need to find the original height $x$ of a leaning tree that forms a right triangle with the ground. 2. **Given:** The hypotenuse (length of the tree) is 20 meters, and the angle between the ground and the tree is $30^\circ$. 3. **Formula:** In a right triangle, the height (opposite side) can be found using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 4. **Apply the formula:** $$\sin(30^\circ) = \frac{x}{20}$$ 5. **Calculate $\sin(30^\circ)$:** $$\sin(30^\circ) = \frac{1}{2}$$ 6. **Set up the equation:** $$\frac{1}{2} = \frac{x}{20}$$ 7. **Solve for $x$ by multiplying both sides by 20:** $$x = 20 \times \frac{1}{2}$$ 8. **Simplify:** $$x = 10$$ **Final answer:** The original height of the tree is $10$ meters.