Algebra problem

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? Include a sketch of the ramp.

Answer 1

The ramp is shaped as a right triangle. One leg is the height of the ramp, the other leg is the horizontal length of the ramp and the hypotenuse is the ramp itself. If x is the horizontal length and the angle is exactly 4.8 degrees, then

tan(4.8)=1.8/x

x=1.8/tan(4.8)

x=21.44 feet

This is the minimum horizontal length. The height can't change, so using a shorter length would increase the angle with the ground beyond 4.8 degrees, and that is not allowed.