1. **Problem statement:** We need to find the length of side AB in a right triangle where angle B is 62°, side AC (opposite angle B) is 12 cm, and the right angle is at A. 2. **Identify the sides:** In the right triangle ABC with right angle at A: - Side AC = 12 cm (opposite angle B) - Side AB is adjacent to angle B - Side BC is the hypotenuse 3. **Use trigonometric ratios:** Since we know the side opposite angle B and want the adjacent side AB, use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, $\theta = 62^\circ$, opposite = 12 cm, adjacent = AB. 4. **Set up the equation:** $$\tan(62^\circ) = \frac{12}{AB}$$ 5. **Solve for AB:** $$AB = \frac{12}{\tan(62^\circ)}$$ 6. **Calculate $\tan(62^\circ)$:** $$\tan(62^\circ) \approx 1.8807$$ 7. **Substitute and simplify:** $$AB = \frac{12}{1.8807}$$ 8. **Intermediate step with cancellation:** $$AB = \frac{\cancel{12}}{\cancel{1.8807}}$$ (showing division) 9. **Final calculation:** $$AB \approx 6.4 \text{ cm}$$ **Answer:** The length of side AB is approximately 6.4 cm to 1 decimal place.