Questions: Question 11, 1.5.143 HW Score: 76.92% Part 1 of 2 Points: 0 of 1 1.5B Homework a. A wheelchair ramp with a length of 75 inches has a horizontal distance of 72 inches. What is the ramp's vertical distance? b. Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of 12 inches. Does this ramp satisfy the requirements? a. The vertical distance of the ramp is

Solution Steps

The problem provides the length of the ramp (\( L = 75 \) inches) and the horizontal distance (\( H = 72 \) inches). We need to find the vertical distance (\( V \)).

The ramp forms a right triangle with the horizontal distance, vertical distance, and the ramp itself as the hypotenuse. The Pythagorean theorem states: \[ L^2 = H^2 + V^2 \] Substitute the known values: \[ 75^2 = 72^2 + V^2 \]

Calculate the squares: \[ 5625 = 5184 + V^2 \] Subtract \( 5184 \) from both sides: \[ V^2 = 5625 - 5184 \] \[ V^2 = 441 \] Take the square root of both sides: \[ V = \sqrt{441} \] \[ V = 21 \]

The construction law states that for every vertical rise of 1 inch, there must be a horizontal run of 12 inches. Calculate the ratio of horizontal run to vertical rise: \[ \text{Ratio} = \frac{H}{V} = \frac{72}{21} \approx 3.4286 \] Compare this to the required ratio of 12: \[ 3.4286 < 12 \] Since the ratio is less than 12, the ramp does not satisfy the construction requirements.

Final Answer