The Uniform Federal Accessibility Standards specify that the ramp angle used for a wheelchair ramp must be less than or equal to 4.78 degrees. All ramps are created to be right triangles. The following diagram shows the parts of a ramp.

Question

If a ramp is built with a ramp length of 16 inches and a vertical rise of 4 inches, what is a possible measurement for the horizontal distance?

(5 points)
Responses

21.9 inches
21.9 inches

5.2 inches
5.2 inches

8.4 inches
8.4 inches

15.5 inches

Answer 1

To find the horizontal distance of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (ramp length) is equal to the sum of the squares of the other two sides (vertical rise and horizontal distance).

Let:

• Ramp length (hypotenuse) = 16 inches
• Vertical rise = 4 inches
• Horizontal distance = \( x \)

According to the Pythagorean theorem: \[ x^2 + (vertical\ rise)^2 = (ramp\ length)^2 \] \[ x^2 + 4^2 = 16^2 \] \[ x^2 + 16 = 256 \] \[ x^2 = 256 - 16 \] \[ x^2 = 240 \] \[ x = \sqrt{240} \approx 15.5\ inches \]

So, the horizontal distance is approximately 15.5 inches.

Thus, the correct response is: 15.5 inches.