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, [tex] AC= 55 [/tex] inches. The top of the seat cushion is 28 inches above the floor. That means, [tex] BC=28 [/tex] inches
We need to find the distance from the base of the ramp to the base of the sofa which is [tex] AB [/tex]
In right angle triangle [tex] ABC [/tex], using Pythagorean theorem...
[tex] 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
[/tex]
So, the distance from the base of the ramp to the base of the sofa rounded to the nearest tenth is 47.3 inches.
