1. **State the problem:** A ladder leans against a wall forming a 60-degree angle with the ground. The height it reaches on the wall is 30 meters. We need to find the length of the ladder. 2. **Formula used:** We use the trigonometric relation for a right triangle: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ where $\theta = 60^\circ$, opposite side is the height of the wall (30 m), and hypotenuse is the ladder length $L$. 3. **Apply the formula:** $$\sin(60^\circ) = \frac{30}{L}$$ 4. **Solve for $L$:** $$L = \frac{30}{\sin(60^\circ)}$$ 5. **Calculate $\sin(60^\circ)$:** $$\sin(60^\circ) = \frac{\sqrt{3}}{2}$$ 6. **Substitute and simplify:** $$L = \frac{30}{\frac{\sqrt{3}}{2}} = 30 \times \frac{2}{\sqrt{3}}$$ 7. **Rationalize the denominator:** $$L = 30 \times \frac{2}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = 30 \times \frac{2\sqrt{3}}{3}$$ 8. **Simplify:** $$L = \frac{60\sqrt{3}}{3} = 20\sqrt{3}$$ 9. **Final answer:** $$\boxed{20\sqrt{3} \text{ meters}}$$ which is approximately 34.64 meters. This means the ladder length is about 34.64 meters to reach 30 meters high on the wall at a 60-degree angle.