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 inch

Answer 1

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

Given:

• Ramp length (hypotenuse) = 16 inches
• Vertical rise (one leg) = 4 inches
• Horizontal distance (the other leg) = ?

Using the Pythagorean theorem:

\[ \text{Ramp length}^2 = \text{Vertical rise}^2 + \text{Horizontal distance}^2 \]

Substituting the known values:

\[ 16^2 = 4^2 + \text{Horizontal distance}^2 \]

This simplifies to:

\[ 256 = 16 + \text{Horizontal distance}^2 \]

Subtracting 16 from both sides:

\[ 256 - 16 = \text{Horizontal distance}^2 \] \[ 240 = \text{Horizontal distance}^2 \]

Now, take the square root of both sides to find the horizontal distance:

\[ \text{Horizontal distance} = \sqrt{240} \approx 15.5 \text{ inches} \]

Thus, the correct answer for a possible measurement of the horizontal distance is:

15.5 inches