Answer
$\frac{\sqrt{2}}{2}$
Work Step by Step
We use the addition formula for sine, $\sin(s+t)=\sin s\cos t+\cos s\sin t$, with $s=18^\circ$ and $t=27^\circ$.
$\sin(18^\circ) \cos(27^\circ)+\cos(18^\circ)\sin(27^\circ)$
$=\sin(18^\circ+27^\circ)$
$=\sin(45^\circ)$
$=\frac{\sqrt{2}}{2}$
