1. **State the problem:** We have a right triangle with one leg measuring 4 cm, an angle of 45°, and the other leg labeled as $x$. We need to find the value of $x$. 2. **Identify the triangle type and formula:** Since one angle is 45° and the triangle is right-angled, this is a 45°-45°-90° triangle. In such triangles, the legs are equal in length. 3. **Use the property of 45°-45°-90° triangles:** The legs are equal, so $x = 4$ cm. 4. **Check with trigonometry:** Using tangent, which is opposite over adjacent, $$\tan(45^\circ) = \frac{x}{4}$$ Since $\tan(45^\circ) = 1$, we have $$1 = \frac{x}{4}$$ 5. **Solve for $x$:** $$x = 4$$ 6. **Final answer:** $x = 4.0$ cm (correct to 1 decimal place).