1. **State the problem:** We need to find the length of the flight of stairs, which is the hypotenuse of a right triangle with a height of 22 m and a base of 39 m. 2. **Formula used:** For a right triangle, the length of the hypotenuse $c$ is given by the Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs of the triangle. 3. **Apply the formula:** Here, $a = 22$ m and $b = 39$ m. $$c = \sqrt{22^2 + 39^2}$$ 4. **Calculate the squares:** $$22^2 = 484$$ $$39^2 = 1521$$ 5. **Sum the squares:** $$484 + 1521 = 2005$$ 6. **Find the square root:** $$c = \sqrt{2005}$$ 7. **Approximate the value:** $$c \approx 44.8$$ m 8. **Round to the nearest meter:** The length of the flight of stairs is approximately 45 meters. **Final answer:** $$\boxed{45 \text{ meters}}$$