1. **State the problem:** We have a right triangle ABC with a right angle at C, angle A is 65 degrees, hypotenuse AB is 7 units, and we need to find the length of side AC. 2. **Formula and rules:** In a right triangle, the side opposite an angle can be found using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, angle A is 65 degrees, side AC is opposite angle A, and AB is the hypotenuse. $$\sin(65^\circ) = \frac{AC}{7}$$ 4. **Solve for AC:** Multiply both sides by 7: $$AC = 7 \times \sin(65^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\sin(65^\circ) \approx 0.9063$$ So, $$AC = 7 \times 0.9063 = 6.3441$$ 6. **Round the answer:** Rounded to the nearest hundredth, $$AC \approx 6.34$$ **Final answer:** The length of side AC is approximately 6.34 units.