1. **State the problem:** We have a right triangle with hypotenuse $45$ miles, one leg $36$ miles, and the other leg $b$ miles unknown. We need to find $b$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. **Apply the formula:** Here, $a = 36$, $b = b$, and $c = 45$. So, $$36^2 + b^2 = 45^2$$ 4. **Calculate squares:** $$1296 + b^2 = 2025$$ 5. **Isolate $b^2$:** $$b^2 = 2025 - 1296$$ $$b^2 = 729$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{729}$$ 7. **Calculate the square root:** $$b = 27$$ **Final answer:** The length of the missing leg $b$ is $27$ miles.