Question

Gena attached a dog ramp to her sofa, which allows her oldest dog to easily climb onto a seat cushion. The ramp is 55 inches long. The top of the seat cushion is 28 inches above the floor.
What is the distance from the base of the ramp to the base of the sofa? Enter your answer, rounded to the nearest tenth.

Answer 1

If we were to view the ramp from its side, the profile would resemble a right triangle with a 90 degree angle where the sofa meets the floor.

In this case, the two legs of the right triangle are 55 inches and 28 inches, and we looking for the length of the hypotenuse.

We can use Pythagorean Theorem which states:

$a^2 + b^2 = c^2$

 where a and b are the legs, and c is the hypotenuse.

$55^2 + 28^2 = c^2$

$3025 + 784 = c^2$

$c^2 = 3809$

$c = \sqrt{3809}$

c = 61.717 inches

To the nearest tenth, the answer is 61.7 inches.