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.
1. To find the horizontal distance, we can use the tangent of the ramp angle.
tan(ramp angle) = vertical rise / horizontal distance
tan(4.75°) = 14 / horizontal distance
horizontal distance = 14 / tan(4.75°) ≈ 175.22 inches
2. Since the sum of the angles in a triangle is 180°, we can find the measure of the third angle by subtracting the given angle from 90° (the measure of a right angle):
Third angle = 90° - ramp angle = 90° - 4.75° = 85.25°
3. To meet the Uniform Federal Accessibility Standards, the shortest side of the triangle will be the vertical rise since it should be less than or equal to the allowed ramp angle.
4. It is not possible to have a horizontal distance of 16 inches because the length of the ramp is given as 3 feet, which is 36 inches. The vertical rise is given as 20 inches. Using the Pythagorean theorem, we can find the horizontal distance:
horizontal distance^2 = length^2 - vertical rise^2
horizontal distance^2 = 36^2 - 20^2
horizontal distance^2 = 1296 - 400
horizontal distance^2 = 896
horizontal distance ≈ 29.93 inches
Therefore, the horizontal distance cannot be 16 inches in this case.