Question

A wheelchair ramp is 20 feet long. It rises 5.1 feet above the ground. What is its angle of inclination (angle of elevation), to the nearest degree​

Answer 1

θ = 15°

Explanation:

The wheelchair ramp creates a right triangle figure. Look at the image I have attached to this response to see the figure.

⭐ What is the "angle of inclination"?

The angle of inclination is the base angle adjacent to the 90-degrees. The angle of inclination is often denoted as θ.

To solve for the angle of inclination, θ, we have to use the inverse of a trigonometric function.

⭐ What trigonometric function do we use?

Look at the side lengths you are given. Are they opposite of θ? Are they adjacent to θ? Are they the hypotenuse of the triangle? Whatever combination of 2 side lengths you have, see what trigonometric function uses those 2 side lengths.

We are given the side length opposite of θ and a side length that is the hypotenuse of the triangle. Therefore, we are going to use the sine function.

⭐ What is the sine function?

sin(θ) = opposite/hypotenuse

Now, we are going to create an equation of the wheelchair ramp using the sine function.

sin(θ) = 5.1/20

Next, find the inverse of the equation. Here is the inverse of the sine function:
`sin^(-1) (opposite/hypotenuse) =`

Let's substitute the opposite and hypotenuse into the inverse of the sine function and solve using a scientific calculator. Make sure to round to the nearest degree.

`sin^(-1)(5.1/20) =`

∴
`sin^(-1)(5.1/20)` ≈ 15°