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

Answer:

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

Step-by-step 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:

$x = \frac{y}{\tan \theta}$ (1)

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

$x = \frac{1\,ft}{\tan 3^{\circ}}$

$x \approx 19.081\,ft$

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