1. **Stating the problem:** We have a right triangle with hypotenuse $d = 5.7$ meters and vertical leg $h = 3$ centimeters. We want to find the length of the horizontal leg. 2. **Convert units:** Since $d$ is in meters and $h$ is in centimeters, convert $h$ to meters for consistency: $$h = 3\text{ cm} = 0.03\text{ m}$$ 3. **Formula used:** In a right triangle, by the Pythagorean theorem: $$d^2 = h^2 + b^2$$ where $b$ is the horizontal leg. 4. **Rearrange to find $b$:** $$b = \sqrt{d^2 - h^2}$$ 5. **Calculate:** $$b = \sqrt{(5.7)^2 - (0.03)^2} = \sqrt{32.49 - 0.0009} = \sqrt{32.4891} \approx 5.7$$ 6. **Interpretation:** The horizontal leg is approximately $5.7$ meters, almost equal to the hypotenuse because the vertical leg is very small compared to the hypotenuse. **Final answer:** $$b \approx 5.7\text{ meters}$$