Wheelchair Ramp Project!

What is the legal angle of elevation for a wheelchair ramp?


          "For commercial use when somebody is sitting in the wheelchair or scooter while it climbs the ramp, ADA recommends a 1:12 slope, which means that every 1" of vertical rise requires at least 1’ (12") of ramp length (5 degrees of incline).Example: A 24" rise requires a minimum ramp length of 24’ (288")." (http://www.discountramps.com/wheelchair-ramp-length/a/B20/)

A visual representation of this ratio is when the vertical leg of a triangle is 1", and the horizontal one is 12".

With these measurements, you can find the angle where the hypotenuse meets the longer leg. You do this using the tangent ratio.

Your starting equation would be:
    Tan(angle x)= 1/12
When your goal is to find the angle from a ratio, you use the inverse functions. So you would put this equation into your calculator:
    Tan^-1=1/12
When you put this into your calculator, you find that the angle is 4.764 degrees, rounded to the nearest thousandth.

What is the angle of elevation of our ramp?

We were able to measure both the ramp's hypotenuse and horizontal length. Because we know both of these, we are able to find the angle of elevation through using the Cosine.

Your original equation would be:
    Cos(angle x)=284/298
To find angles, you must use the inverse function. So you would put this equation in your calculator:
    Cos(angle x)^-1=284/298
You would then find that the measure of the angle is 17.632 degrees, rounded to the nearest thousandth.

Does our ramp meet the requirements?

No! Our ramp is a good 12.868 degrees over the requirement!