1. **State the problem:** We have a right triangle with one leg of length 4 km, a hypotenuse of length 8 km, and the other leg length is unknown, labeled as $b$. 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, $a = 4$ km, $c = 8$ km, and $b$ is unknown. $$4^2 + b^2 = 8^2$$ 4. **Calculate squares:** $$16 + b^2 = 64$$ 5. **Isolate $b^2$:** $$b^2 = 64 - 16$$ $$b^2 = 48$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{48}$$ 7. **Simplify the square root:** $$b = \sqrt{16 \times 3} = 4\sqrt{3}$$ 8. **Approximate the value:** $$b \approx 4 \times 1.732 = 6.928$$ 9. **Round to the nearest tenth:** $$b \approx 6.9 \text{ km}$$ **Final answer:** The length of the missing leg $b$ is approximately 6.9 kilometres.