Santos walks 222 kilometers south and then a certain number of kilometers east. He ends 555 kilometers away from his starting position.
Let the certain number of kilometers east Santos walks be x. We can use the Pythagorean Theorem to relate the distance he walked south, east, and then the total distance. The Pythagorean Theorem states:
a^2 + b^2 = c^2
where a and b are the legs of a right triangle, and c is the hypotenuse.
In this case, the distance Santos walks south is a = 222 km, the distance he walks east is b = x km, and the total distance he is away from his starting position is c = 555 km.
So we have:
222^2 + x^2 = 555^2
Substituting the given values and solving for x:
48964 + x^2 = 308025
Subtract 48964 from both sides:
x^2 = 259061
Take the square root of both sides:
x ≈ 509
Thus, Santos walks approximately 509 kilometers east.