Question

A wheelchair access ramp has an angle elevation of 23 degrees . if the ramp reaches to the top of a 42 inch high porch, how long is the ramp?

Answer 1

We can draw a triangle to describe the situation as shown below:

This is a right triangle, therefore we can use the trigonometric relations on it. We were given one of the angles (23 degrees), the opposite cathetus and we need to find the hypothenuse, therefore we will use the sine relation.

`\begin{gathered} \sin (\alpha)=\frac{\text{ opposite cathetus}}{\text{ hypothenuse}} \\ \sin (23)=\frac{42}{\text{ ramp}} \\ 0.3907=(42)/(ramp) \\ \text{ramp}=(42)/(0.3907)=107.5 \end{gathered}`

The ramp is 107.5 inches long.