Question

in fayetteville, the library is 3 miles west of the post office, and the zoo is 5 miles north of the library. what is the distance from the post office to the zoo? round your response to the nearest mile.

Explanation:

Step1: Identify the right triangle

The library is 3 miles west of the post office, and the zoo is 5 miles north of the library. So the distance from the post office to the library (3 miles) and from the library to the zoo (5 miles) form the legs of a right triangle. The distance from the post office to the zoo is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 3\) and \(b = 5\). So we calculate \(c=\sqrt{3^{2}+5^{2}}=\sqrt{9 + 25}=\sqrt{34}\).

Step3: Calculate and round

\(\sqrt{34}\approx5.83\), and rounding to the nearest mile gives 6.

Answer:

6