1. The problem states that a slide forms a right triangle with a length (hypotenuse) of 9 feet and a height of 8 feet. We need to find the base length. 2. We use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs. 3. Here, let the base be $b$, height be $a = 8$, and hypotenuse $c = 9$. 4. Substitute known values: $$8^2 + b^2 = 9^2$$ 5. Calculate squares: $$64 + b^2 = 81$$ 6. Isolate $b^2$: $$b^2 = 81 - 64$$ 7. Simplify: $$b^2 = 17$$ 8. Take the square root of both sides: $$b = \sqrt{17}$$ 9. Approximate the square root: $$b \approx 4.1231$$ 10. Round to the nearest tenth: $$b \approx 4.1$$ Therefore, the base length is approximately 4.1 feet.