1. **Problem statement:** Find the length of side $a$ in a right triangle where the hypotenuse is 6 and the angle opposite side $a$ is 60°. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 60^\circ$, opposite side is $a$, and hypotenuse is 6, so: $$\sin(60^\circ) = \frac{a}{6}$$ 4. **Solve for $a$:** Multiply both sides by 6: $$a = 6 \times \sin(60^\circ)$$ 5. **Calculate $\sin(60^\circ)$:** $$\sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.8660$$ 6. **Substitute and compute:** $$a = 6 \times 0.8660 = 5.196$$ 7. **Round to the nearest hundredth:** $$a \approx 5.20$$ **Final answer:** $a \approx 5.20$