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Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins $45$ inches from the block and the block is $28$ inches tall, how long is the piece of wood? $\newline$ _____ inches

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Pythagorean Theorem and its converse

Full solution

Q. Tanvi is building a skateboarding ramp by propping the end of a piece of wood on a cinder block. If the ramp begins

45

inches from the block and the block is

28

inches tall, how long is the piece of wood?

\newline

_____ inches

Identify Triangle Formed: Identify the right triangle formed by the ramp, ground, and height of the block. The ground is one leg, the height of the block is the other leg, and the piece of wood is the hypotenuse.
Measurements of Triangle: Ground distance (leg $1$ ): $45$ inches, Height of block (leg $2$ ): $28$ inches, Length of wood (hypotenuse): $x$ inches.
Apply Pythagorean Theorem: Use the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs and $c$ is the hypotenuse.
Plug in Values: Plug in the values: $45^2 + 28^2 = x^2$ .
Calculate Squares: Calculate the squares: $2025 + 784 = x^2$ .
Add Squares: Add the squares: $2025 + 784 = 2809$ .
Find Square Root: Find the square root of $2809$ to solve for $x$ : $\sqrt{2809} = x$ .
Calculate Final Value: Calculate the square root: $x = \sqrt{53}$ .

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