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# Geometry

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The Americans with Disabilities Act stipulates that wheelchair ramps cannot have an incline surpassing a ratio of 1:12. An architect is designing a ramp that allows handicapped persons to get to a door’s level that is 12 feet off the ground. What is the maximum angle of elevation for the ramp, rounded to the nearest hundredth of a degree? What is the shortest possible length of the ramp, rounded to the nearest tenth of a foot?

1: maximum angle of elevation for the ramp

2: Explanation for ramp angle

3: shortest possible length of the ramp

4: Explanation for ramp length

Mar 5, 2019

#1
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Maximum slope for hand-propelled wheelchair ramps should be 1" of rising to every 12" of length (4.8-degree angle; 8.3% grade).

Maximum slope for power chairs should be 1.5" rise to 12" length (7.1-degree angle; 12.5% grade).

Minimum width should be 36" (inside rails) - (48" is ideal).

Mar 5, 2019
#2
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1. The max angle is given by this :

arctan (1/12) = angle  ≈  4.76°

2. The tan is the rise over the run.....hence 1 ft rise / 12 foot run

The tan inverse (arctan) will tell us what an angle with this rise and run is

3. Ramp length can be found by this

sin (4.76°) = 12 / ramp length        .....rearrange as

ramp length =    12/ sin (4.76°) ≈   144.6 ft

4. The sine gives the ratio of the opposite side from the angle to the hypotenuse which is the ramp length   Mar 5, 2019