2. Two joggers run 8 miles north and then 5 miles west.What is the shortest distance, to the nearest mile, they must run to travel to return to their starting point? Draw a picture!

## Step 1<br />The problem describes a right triangle, where the joggers run 8 miles north and then 5 miles west. The shortest distance they must run to return to their starting point is the hypotenuse of this right triangle.<br /><br />## Step 2<br />We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(a\) and \(b\) are the lengths of the two legs of the triangle, and \(c\) is the length of the hypotenuse.<br /><br />## Step 3<br />In this case, \(a = 8\) miles (the distance run north) and \(b = 5\) miles (the distance run west). We can substitute these values into the Pythagorean theorem to find \(c\):<br />### \(c = \sqrt{a^2 + b^2} = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89}\)<br /><br />## Step 4<br />The square root of 89 is approximately 9.43. However, the problem asks for the nearest mile, so we round this to 10 miles.