To find the length of AS, we can use the Pythagorean theorem.

Since triangle ABC is a right triangle with angle ABC=90°, triangle ABD is also a right triangle with angle ABD = 90°.

Using the Pythagorean theorem in triangle ABD:
AD^2 + BD^2 = AB^2
9^2 + 12^2 = AB^2
81 + 144 = AB^2
225 = AB^2
AB = √225
AB = 15 cm

Now, since AS = AB - BS, and we know that BD is perpendicular to AC, AS is the same as AB.
Therefore, AS = 15 cm.