Sine, Cosine, and Tangent

Question

A wheelchair ramp must form an angle no greater than 4.8 degrees with the ground. If a 1.8 foot high ramp is needed, what is the minimum horizontal length for the ramp so it satisfies the angle requirement?

Answer 1

Hello,

To answer a question like this it is often best to draw out your problem. You have a right triangle with a Height of 1.8 feet and an unknown base. The unknown can be called X. You know that the angle must be at least 4.8 Degrees. Once you have drawn this problem out you will be able to notice something important.

Remember the three basic Trigonometric Functions:

Sin = Opposite / Hypotenuse

Cos = Adjacent / Hypotenuse

Tan = Opposite / Adjacent

You have everything you need to solve the problem with some Trigonometry:

Pick the correct function and plug in all the numbers.

Separate the 'Knowns' and 'Unknowns' to opposite sides.

Solve for X.

Good Luck

Answer 2

Let x=horizontal length of the ramp in feet.

If you making an illustration and look at it closely, x is inversely proportional to the angle. Meaning If x is getting longer maintaining 1.8 ft for the height, the angle is getting smaller. Therefore 4.8˚ is the angle we need to use to get the minimum horizontal length of the ramp.

tan θ = _opposite_ = _y_

adjacent x

tan (4.8˚) = 1.8

x

x = ___1.8___ ≈ 21.44 ft.

tan (4.8˚)