This question would be a geometry question. As you can see from the picture attached below, the path taken by the runner forms a right triangle. The 3 miles West would equal the base of the triangle while the 8 miles North will be the side. This means that the hypotenuse (marked by x) is the straight path home that we need to find the value for. We can do this by using the Pythagorean Theorem, which is the following formula
In this formula, the variables a and b are the sides of the triangle, while c is the hypotenuse. Now we can apply the values of the triangle below and solve for c.
9 + 64 =
73 = ... apply square root on both sides
8.54 = x
Finally, we can see that the run straight back home would be 8.54 miles.
