1. **State the problem:** We have a right triangle with one leg of length 15 m, a hypotenuse of length 20 m, and the other leg labeled as $a$. We need to find the length of $a$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $b = 15$ m and $c = 20$ m, so: $$a^2 + 15^2 = 20^2$$ 4. **Calculate squares:** $$a^2 + 225 = 400$$ 5. **Isolate $a^2$:** $$a^2 = 400 - 225$$ $$a^2 = 175$$ 6. **Find $a$ by taking the square root:** $$a = \sqrt{175}$$ 7. **Simplify the square root:** $$a = \sqrt{25 \times 7} = 5\sqrt{7}$$ 8. **Approximate the value:** $$a \approx 5 \times 2.6458 = 13.229$$ **Final answer:** The missing length $a$ is approximately **13.2288 m**.