1. **State the problem:** We have a right triangle ABC with a right angle at C. Side AC is 5 units, and angle A is 40°. We want to find the length of side AB. 2. **Recall the relevant formula:** In a right triangle, the side opposite an angle can be found using the sine function: $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ 3. **Identify sides:** Here, angle A = 40°, opposite side to angle A is BC, adjacent side is AC = 5, and hypotenuse is AB (which we want to find). 4. **Use cosine to find AB:** Since AC is adjacent to angle A, use cosine: $$\cos(40^\circ) = \frac{AC}{AB}$$ 5. **Solve for AB:** $$AB = \frac{AC}{\cos(40^\circ)} = \frac{5}{\cos(40^\circ)}$$ 6. **Calculate:** $$\cos(40^\circ) \approx 0.7660$$ $$AB = \frac{5}{0.7660} \approx 6.53$$ **Final answer:** The length of AB is approximately $6.53$ units.