Question

A wheelchair ramp is 4.2 m long. It rises 0.7 m. What is its angle of inclination to the nearest degree?

Answer 1

`\theta = arcsin (.7/4.2) \approx 10^circ`

Explanation:

We view the ramp as a right triangle. The hypotenuse is 4.2 and the vertical side .7, which is opposite the angle `theta` we seek.

`sin theta = .7/4.2 = 1/6`

I'm going to finish the problem but I'll note if we were actually building the ramp we don't need to know the angle; this sine is sufficient.

`theta = arcsin( 1/6)`

`theta approx 10^circ`

which I think is a pretty steep ramp for a wheelchair.

There will be another inverse sine that is the supplementary angle, around `170^circ`, but we can rule that out as a value for a ramp wedge angle.