Answer
$\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $
Work Step by Step
$\sin {165}=\sin \left( 120+45\right) =\sin {120}\cos 45+\cos {120}\sin 45=\dfrac {\sqrt {3}}{2}\times \dfrac {\sqrt {2}}{2}-\dfrac {1}{2}\dfrac {\sqrt {2}}{2}=\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $
