1. **Problem Statement:** Find the missing leg length in a right triangle given one leg and the hypotenuse. 2. **Formula:** Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$, $b$ are legs. 3. **Given:** One leg $a=4$, hypotenuse $c=14$. Find the other leg $b$. 4. **Step 1:** Rearrange the formula to solve for $b$: $$b^2 = c^2 - a^2$$ 5. **Step 2:** Substitute the known values: $$b^2 = 14^2 - 4^2 = 196 - 16 = 180$$ 6. **Step 3:** Calculate $b$ by taking the square root: $$b = \sqrt{180}$$ 7. **Step 4:** Simplify the square root: $$b = \sqrt{36 \times 5} = 6\sqrt{5}$$ 8. **Step 5:** Approximate to the nearest tenth: $$b \approx 6 \times 2.236 = 13.4$$ **Final answer:** The missing leg length is approximately $13.4$ units.