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Tim likes to skate at a candy store that is due south of his school and due west of his favorite ice cream parlor. If the candy store is \(12\) kilometers from his school and the straight-line distance between the school and the ice cream parlor is \(13\) kilometers, how far is the candy store from the ice cream parlor? $\newline$ ____________Kilometers

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Pythagorean theorem

Full solution

Q. Tim likes to skate at a candy store that is due south of his school and due west of his favorite ice cream parlor. If the candy store is \(12\) kilometers from his school and the straight-line distance between the school and the ice cream parlor is \(13\) kilometers, how far is the candy store from the ice cream parlor?

\newline

____________Kilometers

Identify Distances and Relationship: Identify the distances given and the relationship between the points. Tim's school to the candy store is $12\,\text{km}$ , and the school to the ice cream parlor is $13\,\text{km}$ . The candy store, school, and ice cream parlor form a right triangle with the school at the right angle.
Use Pythagorean Theorem: Use the Pythagorean Theorem to find the distance between the candy store and the ice cream parlor. Let c be the distance from the candy store to the ice cream parlor. We have: $\newline$ $12^2 + c^2 = 13^2$ $\newline$ $144 + c^2 = 169$
Solve for c^ $2$ : Solve for c^ $2$ : $\newline$ $c^2 = 169 - 144$ $\newline$ $c^2 = 25$
Find c: Take the square root of both sides to find c: $\newline$ $c = \sqrt{25}$ $\newline$ $c = 5$

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