1. **Stating the problem:** Construct triangle ABC where side AC = 9 cm, side BC = 7 cm, and angle BAC = 90°. 2. **Understanding the problem:** We have a right triangle with angle BAC = 90°, meaning angle at vertex A is a right angle. 3. **Formula and rules:** In a right triangle, the side opposite the right angle is the hypotenuse. Here, since angle A is 90°, side BC is the hypotenuse. 4. **Check given sides:** Given AC = 9 cm and BC = 7 cm, but BC should be the longest side (hypotenuse) in a right triangle. Since 9 > 7, this contradicts the right angle at A. 5. **Conclusion:** The given data is inconsistent for a right triangle with angle BAC = 90°. For a right triangle at A, BC must be the longest side. 6. **Assuming a typo and swapping sides:** If AC = 7 cm and BC = 9 cm, then we can proceed. 7. **Using Pythagoras theorem:** $AB = \sqrt{BC^2 - AC^2} = \sqrt{9^2 - 7^2} = \sqrt{81 - 49} = \sqrt{32} = 4\sqrt{2}$ cm. 8. **Final answer:** Triangle ABC with AC = 7 cm, BC = 9 cm, angle BAC = 90°, and AB = $4\sqrt{2}$ cm.