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), denoted as $x$. 2. **Formula used:** The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: $$x^2 + 31^2 = 35^2$$ 3. **Apply the formula:** Substitute the known values: $$x^2 + 31^2 = 35^2$$ $$x^2 + 961 = 1225$$ 4. **Isolate $x^2$:** $$x^2 = 1225 - 961$$ $$x^2 = 264$$ 5. **Find $x$ by taking the square root:** $$x = \sqrt{264}$$ 6. **Calculate the square root and round to the nearest tenth:** $$x \approx 16.2481$$ 7. **Check the problem statement:** The answer given is 27.5 feet, which suggests a mistake in the problem setup or values. Re-examining the problem, the building height is 31 feet, ladder length 35 feet, so the distance from the bottom of the ladder to the building is: $$x = \sqrt{35^2 - 31^2} = \sqrt{1225 - 961} = \sqrt{264} \approx 16.2$$ Therefore, the correct distance is approximately 16.2 feet, not 27.5 feet. **Final answer:** The bottom of the ladder is approximately **16.2 feet** from the building.