Answer
$ \dfrac{\sqrt{2+\sqrt{3}}}{2}$
Work Step by Step
$\sin{\dfrac{A}{2}} = \pm \sqrt{\dfrac{1-\cos{A}}{2}}$
$\sin{105} = \sqrt{\dfrac{1-\cos{210}}{2}}= \sqrt{\dfrac{1+\dfrac{\sqrt{3}}{2}}{2}}$
$\sin{105} = \dfrac{\sqrt{2+\sqrt{3}}}{2}$