Question

The doorsill of a campus building is h = 8 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 1/12, as shown in the figure. How long must the ramp be? [The answer is not 96 feet.]

Answer 1

Let's put the y-axis on the door and x-axis 8ft below.

Point: (0,8)
Slope: 1/12

y-8 = (1/12)(x-0) or y = (1/12)x + 8

y = 0

(1/12)x + 8 = 0 or x = -96 -- The ramp hits the ground 96 ft from directly below the door.

Pythagorean Theorem: \(\sqrt{96^{2} + 8^{2}}\)