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To get from home to her friend Kyle's house, Camille would have to walk $3$ miles due north. To get from home to her friend Marcy's house, Camille would have to walk $4$ miles due east. What is the straight-line distance between Kyle's house and Marcy's house? $\newline$ $\_\_\_\_$ miles

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Pythagorean theorem: word problems

Full solution

Q. To get from home to her friend Kyle's house, Camille would have to walk

3

miles due north. To get from home to her friend Marcy's house, Camille would have to walk

4

miles due east. What is the straight-line distance between Kyle's house and Marcy's house?

\newline

\_\_\_\_

miles

Identify Problem Setup: Step $1$ : Identify the problem setup and the right triangle formed. Camille walks $3$ miles north to Kyle's house and $4$ miles east to Marcy's house. These distances form the legs of a right triangle, where the straight-line distance between Kyle's and Marcy's house is the hypotenuse.
Apply Pythagorean Theorem: Step $2$ : Apply the Pythagorean Theorem. $\newline$ Using the formula for the Pythagorean Theorem, $a^2 + b^2 = c^2$ , where $a = 3$ miles and $b = 4$ miles. $\newline$ Calculate $3^2 + 4^2 = c^2$ .
Perform Calculations: Step $3$ : Perform the calculations for the squares of the legs. $\newline$ $3^2 = 9$ and $4^2 = 16$ . $\newline$ Add these to find $c^2$ : $9 + 16 = 25$ .
Solve for Hypotenuse: Step $4$ : Solve for $c$ , the hypotenuse. $\newline$ Take the square root of $25$ to find $c$ . $\newline$ $\sqrt{25} = 5$ .

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