1. **State the problem:** We have a right triangle ABC with a right angle at B. Side AC (the hypotenuse) is 6 units long, and angle A is 29°. We need to find the length of side opposite angle A, labeled $x$, rounded to the nearest hundredth. 2. **Formula used:** In a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse: $$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, angle A = 29°, opposite side = $x$, hypotenuse = 6. $$\sin(29^\circ) = \frac{x}{6}$$ 4. **Solve for $x$:** Multiply both sides by 6: $$x = 6 \times \sin(29^\circ)$$ 5. **Calculate the sine:** Using a calculator, $$\sin(29^\circ) \approx 0.4848$$ 6. **Find $x$:** $$x = 6 \times 0.4848 = 2.9088$$ 7. **Round to the nearest hundredth:** $$x \approx 2.91$$ **Final answer:** $x = 2.91$