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 35 feet long enough for the straight line distance of the ramp to meet the requirements?

What angle of elevation will this ramp have?

Yes, 35 feet is enough The angle of elevation is 4.1º

Explanation:

The ramp, its vertical elevation, and the ground make a right triangle, with the length of the ramp being the hypotenuse, the vertical elevation one leg, and the horizontal distance (ground) the other leg.

The angle of elevation of a ramp is related with the hypotenuse and the opposite leg by the trigonometric ratio named sine:

sine (α) = opposite leg / hypotenuse

In this problem, the length of the ramp. i. e the straight line distance of the ramp, is the hypotenuse, the distance the door is off the ground (the height of the ramp) is the opposite leg, and the angle α is the angle of elevation of the ramp.

Then:

sine (α) = opposite leg / hypotenuse = 2.5 feet / 35 feet ≈ 0.07142857

α = arcsine (0.07142857) = 4.1º.

Thus, the ramp will have an angle of elevation of 4.1º and you conclude that the 35 feet long is enough because the angle is smaller than the limit of 4.8º.