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A piano mover uses a ramp to move a piano into a house. The doorway to the house is 2 feet above the ground and the ramp starts 7 feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.

A piano mover uses a ramp to move a piano into a house. The doorway to the house is $2$ feet above the ground and the ramp starts $7$ feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.

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Pythagorean theorem

Full solution

Q. A piano mover uses a ramp to move a piano into a house. The doorway to the house is

2

feet above the ground and the ramp starts

7

feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.

Identify Triangle: Identify the right triangle formed by the ramp, the height of the doorway, and the distance from the doorway to the base of the ramp. $\newline$ The height of the doorway above the ground represents one leg of the right triangle (vertical leg), and the distance from the doorway to the base of the ramp represents the other leg (horizontal leg). The ramp itself is the hypotenuse of the right triangle.
Apply Pythagorean Theorem: We know: $\newline$ Height of the doorway (vertical leg): $2$ feet $\newline$ Distance from the doorway to the base of the ramp (horizontal leg): $7$ feet $\newline$ Use the Pythagorean Theorem to find the length of the ramp (hypotenuse). $\newline$ The Pythagorean Theorem is $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs of the right triangle and $c$ is the hypotenuse.
Use Given Values: We have: $\newline$ Vertical leg $a$ : $2$ feet $\newline$ Horizontal leg $b$ : $7$ feet $\newline$ Hypotenuse $c$ : ? $\newline$ Plug in the values into the Pythagorean Theorem. $\newline$ $2^2 + 7^2 = c^2$
Calculate Squares: Calculate the squares of the legs. $\newline$ $2^2 = 4$ $\newline$ $7^2 = 49$ $\newline$ Now add these values together. $\newline$ $4 + 49 = 53$ $\newline$ So, $c^2 = 53$
Find Ramp Length: Solve for $c$ by taking the square root of both sides. $c = \sqrt{53}$ Calculate the square root of $53$ to find the length of the ramp. $c \approx 7.28$ (rounded to two decimal places)

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