1. **Problem:** Given a right triangle ABC with a right angle at A, AB = 3 cm, and BC = 6 cm. Find $\sin B$. 2. **Formula:** In a right triangle, $\sin$ of an angle is the ratio of the length of the opposite side to the hypotenuse. 3. **Step 1:** Identify sides relative to angle B. - Opposite side to angle B is $AB = 3$ cm. - Hypotenuse is $BC = 6$ cm. 4. **Step 2:** Calculate $\sin B$ using the formula: $$\sin B = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AB}{BC} = \frac{3}{6}$$ 5. **Step 3:** Simplify the fraction: $$\sin B = \frac{\cancel{3}}{\cancel{6}} = \frac{1}{2}$$ 6. **Answer:** $\sin B = \frac{1}{2}$, which corresponds to option A.