1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 60° angle is 1 meter, and we need to find the side $k$ opposite the 30° angle. 2. **Recall the special right triangle ratios:** In a 30°-60°-90° triangle, the sides are in the ratio: $$1 : \sqrt{3} : 2$$ where 1 is the side opposite 30°, $\sqrt{3}$ opposite 60°, and 2 is the hypotenuse. 3. **Identify given side:** The side opposite 60° is given as 1 meter. According to the ratio, this side corresponds to $\sqrt{3}$ units. 4. **Set up proportion:** Let the common factor be $x$. Then: $$x \sqrt{3} = 1$$ 5. **Solve for $x$:** $$x = \frac{1}{\sqrt{3}}$$ 6. **Find $k$, the side opposite 30°:** $$k = x \times 1 = \frac{1}{\sqrt{3}}$$ 7. **Simplify $k$ to simplest radical form:** $$k = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ **Final answer:** $$k = \frac{\sqrt{3}}{3} \text{ meters}$$