Determine how long the ramp needs to be

Question

To be ADA compliant, wheelchair ramps require no more than a 4.8 degree slope for the ramp.

How long in feet would a ramp need to be to reach a porch that is 36 inches above the ground.

If ramps can be no longer than 30 feet. Can just one ramp be built to reach the porch or would

a landing and another ramp be needed to stay ADA compliant? Show and explain your work

using mathematical language from this course

Answer 1

Sin(4.8) = 36/x

36 = sin(4.8)x

then divide both sides by sin(4.8)

36/sin(4.8) = x

Sin(4.8) is 0.084 rounded to 3 decimal places

therefore 36/0.084 = x

428.6 inches (to 1 decimal place) so now we have to convert our answer from inches to feet.

428.6/12 which is 35.7 feet to the nearest tenth or 1 decimal place.

This length 35.7ft is longer than the 30 ft so we will need more than one ramp to stay ADA compliant.

Answer 2

The first thing you want to do is draw a picture and label what you know.

-         Since the restriction on length is in feet, you should convert the 36 in high porch to 3 feet in height.

-         Since they are asking for the length of the ramp, x should be on the slanted slide of the triangle, i.e. on the hypotenuse.

 

The 3 ft side is the Opposite Side relative to the angle at the bottom, and x is the hypotenuse. Since sine uses opposite and hypotenuse, we use sine:

sin 4.8 = 3/x

x (sin 4.8) = 3                    Multiply each side by x.

x = 3/(sin 4.8)                   Divide each side by sin 4.8

x = 35.85 feet

Since ramps cannot be longer than 30 feet, you must use 2 ramps with a landing between them.

Answer 3

36/x = tan 4.8

x=36/tan4.8= about 36/.084

x= about 428.7 inches = 428.7/12

= about 35.7 feet needed for the ramp