Final answer:
To find BA, we need to use the Pythagorean theorem. Substituting the given values and simplifying the equation, we get BA = 5.
Step-by-step explanation:
To find BA, we need to use the Pythagorean theorem since it is a right triangle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, AC is the hypotenuse, and AD and DC are the other two sides. So we have AD^2 + DC^2 = AC^2. Substituting the given values, we get 12^2 + 5^2 = 13^2.
Simplifying this equation, we get 144 + 25 = 169. Therefore, BA^2 = 169 - 144 = 25. Taking the square root of both sides, we get BA = 5.