Question

The doorsill of a campus building is h = 7 feet above ground level. To allow wheelchair access, the steps in front of the door are to be replaced by a straight ramp with constant slope 1/10, as shown in the figure. How long must the ramp be?

Answer 1

In order to figure out this problem, you must first find out how far away the bottom of this ramp will be from the building. You have a slope of 1/10, so for every height increase of 1 foot, you go forward 10 feet. Using this logic, after increasing the height by 7 feet, the distance between the beginning of the ramp to the bottom of the wall is 70 feet... However, you want to know the length of the ramp, not how far the bottoms are from each other. If you were to draw a figure, you would see that the ramp is a right triangle. This means that you can use the pythagorean theorem.

`a^2+b^2=c^2, 7^2+70^2=c^2`
You just have to solve for c and that will be the length of the ramp

Answer 2

The ramp must be 70.35 ft.

Explanation:

A rectangle triangle is formed. The ramp is the hypotenuse and h = 7 ft is the side opposite to the slope = 1/10. This slope means: for each vertical step there are 10 horizontal steps (is the same definition of line's slope). Writing that in a equation gives :

slope = 1/10 = (opposite side)/(adjacent side)

adjacent side = 10*(opposite side)

adjacent side = 10*7 ft

adjacent side = 70 ft

Pythagorean theorem states

hypotenuse^2 = side^2 + side^2

hypotenuse^2 = 7^2 + 70^2

hypotenuse = sqrt(4949)

hypotenuse = 70.35 ft