1. **State the problem:** We have a right triangle with a 50° angle and hypotenuse length 8. We need to find the length of side $a$, which is opposite the 50° angle. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 50^\circ$, opposite side is $a$, and hypotenuse is 8, so: $$\sin(50^\circ) = \frac{a}{8}$$ 4. **Solve for $a$:** Multiply both sides by 8: $$a = 8 \times \sin(50^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\sin(50^\circ) \approx 0.7660$$ So, $$a \approx 8 \times 0.7660 = 6.128$$ 6. **Final answer:** The length of side $a$ is approximately $$a \approx 6.13$$ (rounded to two decimal places).