1. **State the problem:** We have a right triangle with angles 30° and 60°, the side opposite the 30° angle is given as $7\sqrt{3}$ cm, and we need to find the hypotenuse $w$. 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 the shortest side (length $x$), - The side opposite 60° is $x\sqrt{3}$, - The hypotenuse is $2x$. 3. **Identify the given side:** The side opposite 30° is $7\sqrt{3}$ cm, so this corresponds to $x$. 4. **Set up the equation:** Since the side opposite 30° is $x$, we have: $$x = 7\sqrt{3}$$ 5. **Find the hypotenuse $w$:** The hypotenuse is $2x$, so: $$w = 2x = 2 \times 7\sqrt{3} = 14\sqrt{3}$$ 6. **Final answer:** The hypotenuse $w$ is $14\sqrt{3}$ centimeters.