1. **State the problem:** We have a right triangle with one leg measuring 1 cm and the hypotenuse measuring 2 cm. We need to find the length of the other leg. 2. **Formula used:** The Pythagorean theorem states that in a right triangle, $$\text{leg}_1^2 + \text{leg}_2^2 = \text{hypotenuse}^2$$ where $\text{leg}_1$ and $\text{leg}_2$ are the legs, and the hypotenuse is the longest side. 3. **Apply the values:** Let the unknown leg be $x$. Then, $$1^2 + x^2 = 2^2$$ which simplifies to $$1 + x^2 = 4$$ 4. **Isolate $x^2$:** $$x^2 = 4 - 1$$ $$x^2 = 3$$ 5. **Solve for $x$ by taking the square root:** $$x = \sqrt{3}$$ 6. **Approximate the value:** $$x \approx 1.732$$ 7. **Round to the nearest tenth:** $$x \approx 1.7$$ **Final answer:** The length of the other leg is approximately **1.7 cm**.