Question

Safe wheelchair ramp specifications require about 4.75° maximum angle to be constructed with the ground. At a particular building, the owner is installing a wheelchair ramp that needs to rise 1 feet off the ground. The owner insists on constructing the angle with the ground at 3°. How much horizontal distance will the ramp cover with these specifications?

Answer 1

The ramp must cover a horizontal distance of approximately 19.081 feet.

Explanation:

Given the vertical distance (
`y`), measured in feet, and the angle of the wheelchair ramp (
`\theta`), measured in sexagesimal degrees. The horizontal distance needed for the ramp (
`x`), measured in feet, is estimated by the following trigonometrical expression:

`x = (y)/(\tan \theta)` (1)

If we know that
`y = 1\,ft` and
`\theta = 3^(\circ)`, then the horizontal distance covered by this ramp is:

`x = (1\,ft)/(\tan 3^(\circ))`

`x \approx 19.081\,ft`

The ramp must cover a horizontal distance of approximately 19.081 feet.