1. **State the problem:** We have a ladder leaning against a building forming a right triangle. The ladder is the hypotenuse of length 35 feet, the building height is one leg of length 31 feet, and we want to find the distance from the bottom of the ladder to the building (the other leg). 2. **Formula used:** The Pythagorean theorem states: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the right triangle. 3. **Assign values:** $$c = 35, \quad a = 31, \quad b = ?$$ 4. **Rearrange to solve for $b$:** $$b^2 = c^2 - a^2$$ 5. **Calculate squares:** $$b^2 = 35^2 - 31^2 = 1225 - 961 = 264$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{264}$$ 7. **Simplify and approximate:** $$b \approx 16.2481$$ 8. **Round to the nearest tenth:** $$b \approx 16.2$$ **Final answer:** The bottom of the ladder is approximately 16.2 feet from the base of the building.