Question

1. ashley jogged 3.4 miles east, then 5.7 miles south. how far is ashley from her starting point?

Explanation:

Step1: Apply the Pythagorean theorem

The distance Ashley jogged east and south forms the legs of a right - triangle. Let \(a = 3.4\) and \(b=5.7\). The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the distance from the starting point.
So, \(c^{2}=(3.4)^{2}+(5.7)^{2}\).
Calculate \((3.4)^{2}=3.4\times3.4 = 11.56\) and \((5.7)^{2}=5.7\times5.7=32.49\).
Then \(c^{2}=11.56 + 32.49=44.05\).

Step2: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{44.05}\approx6.64\) (rounded to two decimal places).

Answer:

Ashley is approximately \(6.64\) miles from her starting point.