Question

1. if you run 5 miles north and then 6 miles west, what is the shortest distance between where you started and where you finished? draw a picture and show your work. round to the nearest hundredth. type a response

Explanation:

Step1: Recognize right - triangle

The north - south and west - east movements form a right - triangle. The two legs of the right - triangle are $a = 5$ miles and $b=6$ miles.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$, where $c$ is the hypotenuse (the shortest distance between the start and end points). Substitute $a = 5$ and $b = 6$ into the formula: $c=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}$.

Step3: Calculate and round

$\sqrt{61}\approx 7.81$ miles.

Answer:

$7.81$ miles