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In Rosewood City, the library is $6.5$ miles due south of the courthouse and $3.4$ miles due west of the community swimming pool. What is the distance between the courthouse and the community swimming pool? $\newline$ If necessary, round your answer to the nearest tenth. $\newline$ ____ miles $\newline$

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Pythagorean theorem

Full solution

Q. In Rosewood City, the library is

6.5

miles due south of the courthouse and

3.4

miles due west of the community swimming pool. What is the distance between the courthouse and the community swimming pool?

\newline

If necessary, round your answer to the nearest tenth.

\newline

____ miles

\newline

Identify Triangle Legs: Identify the legs of the right triangle formed by the library, courthouse, and community swimming pool. The library is $6.5$ miles south of the courthouse and $3.4$ miles west of the pool.
Apply Pythagorean Theorem: Apply the Pythagorean Theorem to find the distance between the courthouse and the swimming pool. Let $c$ be the distance we need to find. $c^2 = 6.5^2 + 3.4^2$
Calculate Leg Squares: Calculate the squares of the legs. $\newline$ $6.5^2 = 42.25$ $\newline$ $3.4^2 = 11.56$
Add Leg Squares: Add the squares of the legs. $\newline$ $42.25 + 11.56 = 53.81$
Find Distance: Take the square root of the sum to find $c$ . $\sqrt{53.81} \approx 7.3$

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