Answer
$$\frac{{\sqrt {4 - {x^2}} }}{2}$$
Work Step by Step
$$\eqalign{
& {\text{From the triangle bellow we have that}} \cr
& \sin \theta = \frac{{{\text{Opposite side}}}}{{{\text{Hypotenuse}}}} \cr
& \sin \theta = \frac{{\sqrt {4 - {x^2}} }}{2} \cr
& and \cr
& {\text{cos}}\theta = \frac{x}{2} \cr
& \theta = {\cos ^{ - 1}}\left( {\frac{x}{2}} \right) \cr
& \cr
& {\text{Then,}} \cr
& \sin \theta = \sin \left( {{{\cos }^{ - 1}}\left( {\frac{x}{2}} \right)} \right) \cr
& \sin \theta = \frac{{\sqrt {4 - {x^2}} }}{2} \cr} $$
