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Question

The doorsill of a campus building is h = 6 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? [The answer is not 60 feet.

Answer 1

The ramp must start 60 feet from the door, but the ramp itself is the HYPOTENUSE of the triangle formed by the height of the doorsill and the distance from the door to the start of the ramp.

 

By the Pythagorean theorem, 6² + 60² = the square of the length of the ramp.

 

6² + 60² = 36 + 3600 = 3636.  So the length of the ramp is the square root of 3636, or 60.3 feet.