Question

Federal standards require that the angle ramp for the wheel chair to be less than 5 degrees, if the length of the ramp is 20 feet and vertical rise is 15 inches, does it meet federal standards?

Answer 1

The ramp does meet federal standards

Explanation:

The first thing we must do is sketch the situation of the statement in order to better understand it.

Now, we need to convert feet to inches, so they are the same units. We know that 1 foot is equal to 12 inches, so:

1 ft = 12 in

20 ft = 20 ft *12 in/ft = 240 in

Now, we calculate the angle of the ramp by means of the trigonometric sine function that relates the side opposite the angle to the hypotenuse.

Therefore:

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{ opposite = 15} \\ \text{ hypotenuse = 240} \\ \text{ Replacing} \\ \sin \theta=(15)/(240) \\ \theta=\arcsin \mleft((15)/(240)\mright) \\ \theta=3.58\text{\degree} \end{gathered}`

The value of the angle is 3.58°, which is less than 5°, which means that it meets federal standards.