Finding Length of Side in Triangle using Law of Sines

In triangle ABC, angle A measures 60 degrees, angle B measures 75 degrees, and side AC is 12 units long. Calculate the length of side AB to the nearest hundredth of a unit.

Use the Law of Sines, which states that:

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

where \(a, b, c\) are the lengths of sides opposite to angles A, B, and C respectively.

Note: Round your final answer to the nearest hundredth.