To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, AC is the hypotenuse, and AB and BC are the other two sides.
Using the Pythagorean theorem:
AC^2 = AB^2 + BC^2
AC^2 = 9^2 + 19^2
AC^2 = 81 + 361
AC^2 = 442
Taking the square root of both sides to find the length of AC:
AC = √442
AC ≈ 21.03
Therefore, the length of AC is approximately 21.03.
None of the provided answer options (28, 9, 19, 10) match the calculated length.