1. **Stating the problem:** We have a right triangle with a right angle, one angle of 60°, and the hypotenuse labeled 30. We need to find the lengths of sides $x$ and $y$. 2. **Recall the properties of a 30°-60°-90° triangle:** In such a triangle, the sides are in the ratio: $$1 : \sqrt{3} : 2$$ where the side opposite 30° is $1$, opposite 60° is $\sqrt{3}$, and the hypotenuse is $2$. 3. **Assign the sides according to the problem:** - Hypotenuse = 30 - Side opposite 60° = $y$ - Side opposite 30° = $x$ 4. **Use the ratio to find $x$ and $y$:** Since hypotenuse corresponds to $2$, we have: $$\text{scale factor} = \frac{30}{2} = 15$$ 5. **Calculate $x$ (opposite 30°):** $$x = 1 \times 15 = 15$$ 6. **Calculate $y$ (opposite 60°):** $$y = \sqrt{3} \times 15 = 15\sqrt{3}$$ **Final answer:** $$x = 15, \quad y = 15\sqrt{3}$$