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, in the box.

Answer 1

The correct answer should be 47.3

Answer 2

The distance from the base of the ramp to the base of the sofa rounded to the nearest tenth is 47.3 inches.

Explanation

According to the diagram, length of the ramp is, $AC= 55$ inches. The top of the seat cushion is 28 inches above the floor. That means, $BC=28$ inches

We need to find the distance from the base of the ramp to the base of the sofa which is $AB$

In right angle triangle $ABC$, using Pythagorean theorem...

$AC^2 = AB^2 + BC^2\\ \\ (55)^2= AB^2 + (28)^2 \\ \\ AB^2 = (55)^2 - (28)^2 \\ \\ AB^2 = 3025 - 784\\ \\ AB^2 = 2241\\ \\ AB = \sqrt{2241}= 47.3$

So, the distance from the base of the ramp to the base of the sofa rounded to the nearest tenth is 47.3 inches.