The Uniform Federal Accessibility Standards specify that the ramp angle used for a wheelchair ramp must be less than or equal to 4.78°
. All ramps are created to be right triangles. The following diagram shows the parts of a ramp.
The longest leg of a right triangle is labeled horizontal distance. The hypotenuse is labeled length of ramp. The angle opposite the short leg is labeled ramp angle. The short leg is labeled vertical rise.
If the length of the ramp is 16 inches and the vertical rise is 14 inches, what is a possible measurement for the horizontal distance?
If the ramp angle is 4.75°
, determine the measure of the third angle of the triangle.
To meet the Uniform Federal Accessibility Standards, which side will be the shortest side of the triangle?
The length of a ramp is 3 feet long and its vertical rise is 20 inches. Explain why it is or is not possible to have a horizontal distance of 16 inches.
To find the possible measurement for the horizontal distance, we can use trigonometry. The formula to find the horizontal distance (adjacent side) in a right triangle is:
horizontal distance = vertical rise / tan(ramp angle)
horizontal distance = 14 / tan(4.75°)
horizontal distance ≈ 14 / 0.0839
horizontal distance ≈ 166.6 inches
Therefore, a possible measurement for the horizontal distance is approximately 166.6 inches.
To find the measure of the third angle of the triangle, we can subtract the given ramp angle from 90° since the sum of all angles in a triangle is 180°. Therefore, the third angle is:
third angle = 90° - 4.75°
third angle ≈ 85.25°
To meet the Uniform Federal Accessibility Standards, the shortest side of the triangle will be the horizontal distance. This is because the ramp angle must be less than or equal to 4.78°, so the vertical rise cannot be longer than the horizontal distance.
For a ramp length of 3 feet (36 inches) and a vertical rise of 20 inches, it is not possible to have a horizontal distance of 16 inches. This is because the vertical rise is already 20 inches, which is longer than the desired horizontal distance of 16 inches. The ramp cannot physically be constructed in this way.