Mr. Romero attached a ramp to the base of a window sill so that the family cat could more easily climb onto it. The ramp is 84 inches long. The window sill is 50 inches above the floor. ?

What is the distance from the base of the ramp to the base of the wall?

Enter your answer, rounded to the nearest tenth, in the box.

1 Answer
Math Tutor
May 24, 2018

#x = sqrt(84^2 - 50^2) = sqrt( 7056 - 2500) = 67.5# inches

Explanation:

The ramp forms a right triangle, where
the ramp (84") is the hypotenuse #h#
the floor, from the base of the ramp to the wall, is side #x#
and the wall, from the floor to the window sill (50"), is side #y#

The relationship between the 3 sides is:
#h^2 = x^2 + y^2#
Since we know the length of #h# and #y#, we can determine #x# .
#x^2 = h^2 - y^2#
#x = sqrt(h^2 - y^2)#
#x = sqrt(84^2 - 50^2) = sqrt( 7056 - 2500) = 67.5# inches

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