1. **State the problem:** We need to find the horizontal distance of a wheelchair ramp with a vertical rise of 8 inches and an incline angle of 4.76°. 2. **Relevant formula:** In a right triangle, the tangent of the incline angle $\theta$ relates the opposite side (vertical rise) to the adjacent side (horizontal distance) as: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** Here, $\theta = 4.76^\circ$, opposite side = 8 inches, and adjacent side = horizontal distance $x$ (unknown). $$\tan(4.76^\circ) = \frac{8}{x}$$ 4. **Solve for $x$:** $$x = \frac{8}{\tan(4.76^\circ)}$$ 5. **Calculate $\tan(4.76^\circ)$:** $$\tan(4.76^\circ) \approx 0.0832$$ 6. **Substitute and compute:** $$x = \frac{8}{0.0832} \approx 96.2$$ 7. **Label the ramp dimensions:** - Incline angle: $4.76^\circ$ - Vertical rise: 8 inches - Horizontal distance: approximately 96.2 inches **Final answer:** The horizontal distance to minimize the ramp length is approximately **96.2 inches**.