1. **State the problem:** We have a right triangle with a vertical leg of length 9.7 km, a hypotenuse of length 9.4 km, and a missing horizontal leg $b$. We need to find $b$. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Identify known values:** Here, $a = 9.7$ km, $c = 9.4$ km, and $b$ is unknown. 4. **Apply the formula:** Substitute the known values: $$9.7^2 + b^2 = 9.4^2$$ 5. **Calculate squares:** $$94.09 + b^2 = 88.36$$ 6. **Isolate $b^2$:** $$b^2 = 88.36 - 94.09$$ $$b^2 = -5.73$$ 7. **Interpretation:** Since $b^2$ is negative, this means the given side lengths cannot form a right triangle (the hypotenuse must be the longest side). Therefore, the problem as stated has no real solution for $b$. **Final answer:** No real length $b$ exists because the hypotenuse length must be greater than both legs, but here it is shorter than one leg.