1. **State the problem:** We have a right triangle with legs of lengths 8 meters and 4 meters, and the hypotenuse labeled as $b$. We need to find the length of $b$. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$b^2 = a^2 + c^2$$ where $b$ is the hypotenuse and $a$, $c$ are the legs. 3. **Apply the formula:** Here, $a = 8$ and $c = 4$, so: $$b^2 = 8^2 + 4^2$$ $$b^2 = 64 + 16$$ $$b^2 = 80$$ 4. **Solve for $b$:** $$b = \sqrt{80}$$ 5. **Simplify the square root:** $$b = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$ 6. **Calculate the decimal value:** $$b \approx 4 \times 2.236 = 8.944$$ 7. **Round to the nearest tenth:** $$b \approx 8.9$$ meters **Final answer:** The length of the missing leg $b$ is approximately **8.9 meters**.