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On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is $40$ feet and the distance between the tire swing and the monkey bars is $50$ feet, how far is the slide from the monkey bars? $\newline$ $\_\_\_\_\_\_\_$ feet

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Pythagorean theorem

Full solution

Q. On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is

40

feet and the distance between the tire swing and the monkey bars is

50

feet, how far is the slide from the monkey bars?

\newline

\_\_\_\_\_\_\_

feet

Identify Triangle: Identify the right triangle with the slide, tire swing, and monkey bars as the vertices.
Use Pythagorean Theorem: Use the Pythagorean Theorem: $a^2 + b^2 = c^2$ , where $a$ is the distance between the slide and the tire swing, $b$ is the distance between the tire swing and the monkey bars, and $c$ is the distance between the slide and the monkey bars.
Plug in Distances: Plug in the known distances: $40^2 + 50^2 = c^2$ .
Calculate Squares: Calculate the squares: $1600 + 2500 = c^2$ .
Add Squares: Add the squares: $1600 + 2500 = 4100$ .
Solve for c: Solve for c by taking the square root of $4100$ : $c = \sqrt{4100}$ .
Calculate Square Root: Calculate the square root: $c = \sqrt{4100} = 64$ .

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