1. **Problem statement:** We need to find the length of the hypotenuse in a right-angled triangle where one angle is 60° and the side adjacent to this angle is 6 meters. 2. **Formula used:** In a right-angled triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 60^\circ$ and the adjacent side is 6 m. Let the hypotenuse be $h$. $$\cos(60^\circ) = \frac{6}{h}$$ 4. **Calculate $\cos(60^\circ)$:** $$\cos(60^\circ) = \frac{1}{2}$$ 5. **Set up the equation:** $$\frac{1}{2} = \frac{6}{h}$$ 6. **Solve for $h$:** Multiply both sides by $h$: $$\frac{1}{2}h = 6$$ Multiply both sides by 2: $$h = 12$$ 7. **Final answer:** The length of the hypotenuse is $12$ meters. This is already in its simplest form.