\[\sin{33{^\circ}} \cdot \cos{27{^\circ}} =\]
\[= \frac{1}{2} \cdot \left( \sin{60{^\circ}} + \sin{6{^\circ}} \right) =\]
\[= \frac{1}{2} \cdot \left( \frac{\sqrt{3}}{2} + \sin{6{^\circ}} \right) =\]
\[= \frac{\sqrt{3}}{4} + \frac{1}{2}\sin{6{^\circ}}\]