1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 60° angle (the hypotenuse) is 5 inches, and we need to find the length of side $s$, which is opposite the 30° angle. 2. **Recall the properties of a 30°-60°-90° triangle:** The sides are in the ratio $1 : \sqrt{3} : 2$, where: - The side opposite 30° is $x$ - The side opposite 60° is $x\sqrt{3}$ - The hypotenuse (opposite 90°) is $2x$ 3. **Identify the hypotenuse:** Given the side adjacent to 60° is 5 inches, and since the hypotenuse is opposite 90°, the 5 inches corresponds to the hypotenuse. 4. **Set up the equation:** Since hypotenuse $= 2x = 5$, solve for $x$: $$2x = 5$$ 5. **Solve for $x$:** $$x = \frac{5}{2}$$ 6. **Find $s$ (side opposite 30°):** $$s = x = \frac{5}{2}$$ 7. **Express $s$ in simplest radical form:** Since $\frac{5}{2}$ is already simplest, the answer is: $$s = \frac{5}{2}$$ inches. **Final answer:** $s = \frac{5}{2}$ inches.