To find the distance the woman is from her home, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the woman walked 3 miles due East and 4 miles due South, forming a right triangle.
The distance from her home to the point where she ended up can be calculated as follows:
Distance = √(3^2 + 4^2)
Distance = √(9 + 16)
Distance = √25
Distance = 5 miles
Therefore, the woman is 5 miles away from her home.