1. **Problem:** Find the value of side AB in a right triangle with vertices A, B, C, where angle B is 90°, AC = 12, and angle C = 62°. 2. **Formula:** Use the sine function in a right triangle: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Identify sides:** Here, AB is opposite angle C, AC is the hypotenuse. 4. **Apply formula:** $$\sin(62^\circ) = \frac{AB}{12}$$ 5. **Solve for AB:** $$AB = 12 \times \sin(62^\circ)$$ 6. **Calculate:** Using a calculator, $$\sin(62^\circ) \approx 0.8829$$ 7. **Final value:** $$AB = 12 \times 0.8829 = 10.5948$$ 8. **Round:** To the nearest tenth, $$AB \approx 10.6$$ **Answer:** The length of AB is approximately 10.6.