1. **Problem Statement:** We have a right triangle with a 30° angle. The side adjacent to the 30° angle is 12, the hypotenuse is $b$, and the side opposite the 30° angle is $a$. We need to find $a$. 2. **Relevant Formula:** In a right triangle, the side opposite 30° is half the hypotenuse, and the side adjacent to 30° is $\frac{\sqrt{3}}{2}$ times the hypotenuse. 3. Since the side adjacent to 30° is 12, we use: $$12 = b \times \frac{\sqrt{3}}{2}$$ 4. Solve for $b$: $$b = \frac{12 \times 2}{\sqrt{3}} = \frac{24}{\sqrt{3}}$$ 5. The side opposite 30° is half the hypotenuse: $$a = \frac{b}{2} = \frac{1}{2} \times \frac{24}{\sqrt{3}} = \frac{12}{\sqrt{3}}$$ 6. To rationalize the denominator: $$a = \frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{12\sqrt{3}}{3} = 4\sqrt{3}$$ **Final answer:** $$a = 4\sqrt{3}$$