The distance from the base of the ramp to the base of the sofa rounded to the nearest tenth exists at 47.3 inches.
Pythagorean theorem
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle exists equivalent to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2} + b^{2} = c^{2}[/tex]
According to the diagram, the length of the ramp exists, AC=55 inches. The top of the seat cushion exists 28 inches above the floor. That means, BC=28 inches require to find the distance from the base of the ramp to the base of the sofa which is AB
In a right-angle triangle, ABC, using the Pythagorean theorem.
[tex]$A C^{2}=A B^{2}+B C^{2}$[/tex]
[tex]$(55)^{2}=A B^{2}+(28)^{2}$[/tex]
[tex]$A B^{2}=(55)^{2}-(28)^{2}$[/tex]
[tex]$A B^{2}=3025-784$[/tex]
[tex]$A B^{2}=2241$[/tex]
[tex]$A B=\sqrt{2241}=47.3 < b r / > $[/tex]
So, the distance from the base of the ramp to the base of the sofa rounded to the nearest tenth exists at 47.3 inches.
To learn more about Pythagorean theorem refer to:
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