To find the length of AB, we can use trigonometry.

Given that ∠A = 60°, we can find that ∠B = 180° - 90° - 60° = 30°.

Now, we have a right triangle ABC where ∠C = 90°, ∠A = 60°, and ∠B = 30°.

We can use the trigonometric ratios in a right triangle:
sin 60° = opposite/hypotenuse
cos 60° = adjacent/hypotenuse
tan 60° = opposite/adjacent
sin 30° = opposite/hypotenuse
cos 30° = adjacent/hypotenuse
tan 30° = opposite/adjacent

Since we are looking to find AB, which is the side opposite to angle ∠A (60°), we will use the sin 60° ratio.

sin 60° = AB/AC
sin 60° = AB/(AB + 15)
AB = 15 * sin 60° / sin 60°
AB = 15 cm

Therefore, the length of AB is 15 cm.