Final answer:
To find the distance the runner is from the starting point when running straight back, we use the Pythagorean theorem on the right-angled path created by 2 miles east and 4 miles north, which yields a direct distance of 2√5 miles.
Step-by-step explanation:
If a runner jogs 2 miles east and then jogs 4 miles north, we can visualize the runner's path as a right-angled triangle, where the two paths (east and north) represent the perpendicular sides of the triangle. To find out how far the runner is from her starting point when running straight back, we need to calculate the hypotenuse of the triangle, which represents the direct distance back to the starting point.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c^2 = a^2 + b^2. Substituting the given values, we get:
c^2 = 2^2 + 4^2
c^2 = 4 + 16
c^2 = 20
To find c, we take the square root of 20:
c = √20
Since √20 can be simplified to 2√5, the runner is 2√5 miles away from her starting point if she plans to run straight back.