Question

In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8∘. A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.

Is 25 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?

Answer 1

Answer:

ADA Ramp Specifications Require a 1:12 ramp slope ratio which equals 4.8 degrees slope or one foot of wheelchair ramp for each inch of rise.

Answer 2

given angle of elevation and distance of door of the ground, find the possible length of ramp to meet the requirements of ADA

Explanation:

1. in a right angled triangle having angle θ then,  $sin\theta = \frac{P}{H}$  
2. here the ground, distance off the ground to door (P) and the length of ramp (H) are forming a right angled and Angle of elevation θ.
3. given that $\theta_{max}=4.8$°  then we have,                                            $sin(\theta_{max}) = sin4.8$°$=0.084(approx)$     ---(a)
4. given $P=2.5\ ft.$ we get minimum possible length of ramp as,                              $sin\theta=\frac{P}{H} \\0.084=\frac{2.5}{H} \\H_{min}=29.76\ ft.$    
5. hence $25\ ft$  is not enough for the length of ramp . Angle of elevation with this length is,  $\theta = sin^{-1}(\frac{2.5}{25} )$                                                                                                                                              

                                        $\theta = 5.74$° (approx.)