Question

order to meet the 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 30 ft long enough for the straight-line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?*BLANK*a 30-foot ramp, will have an angle of elevation of approximately *BLANK*

Answer 1

In order to meet the ADA 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 30 ft long enough for the straight-line distance of the ramp to meet the requirements?

What angle of elevation will this ramp have?

Let us draw a diagram to better understand the problem

As you can see, with respect to the angle of elevation (θ), the opposite side is 2.5 ft and the adjacent side is 30 ft

Recall from the trigonometric ratios

$\tan \theta=\frac{\text{opposite}}{\text{adjacent}}$

Let us substitute given values into the above formula

$\begin{gathered} \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \\ \tan \theta=\frac{2.5}{30} \\ \theta=\tan ^{-1}(\frac{2.5}{30}) \\ \theta=4.76\degree \\ \theta=4.8\degree\quad (\text{rounding off)} \end{gathered}$

So, 30 ft is long enough for the straight-line distance of the ramp to meet the requirements.

The angle of elevation is not more than 4.8° which meets the ADA (Americans with Disabilities Act) requirements.

Yes, a 30-foot ramp, will have an angle of elevation of approximately 4.8°