1. **Problem statement:** We have a right triangle with hypotenuse $a$, opposite side to the 30° angle is 7, and adjacent side $b$ to be found. 2. **Formula and rules:** In a right triangle, the side opposite an angle $\theta$ is related to the hypotenuse by $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ and the adjacent side by $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. 3. **Find hypotenuse $a$ using opposite side and sine:** $$\sin(30^\circ) = \frac{7}{a}$$ Since $\sin(30^\circ) = \frac{1}{2}$, $$\frac{1}{2} = \frac{7}{a} \implies a = 7 \times 2 = 14$$ 4. **Find adjacent side $b$ using cosine:** $$\cos(30^\circ) = \frac{b}{a}$$ Since $\cos(30^\circ) = \frac{\sqrt{3}}{2}$, $$\frac{\sqrt{3}}{2} = \frac{b}{14} \implies b = 14 \times \frac{\sqrt{3}}{2} = 7\sqrt{3}$$ 5. **Answer:** The side $b$ is $7\sqrt{3}$. This means the horizontal leg $b$ is $7\sqrt{3}$ units long.