Answer
$$\sin \theta = \frac{x}{{\sqrt {{x^2} + 16} }}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}x = 4\tan \theta ,{\text{ then }} \cr
& \tan \theta = \frac{x}{4} = \frac{{{\text{Opposite side}}}}{{{\text{Adjacent side}}}} \cr
& {\text{Hypotenuse}} = \sqrt {{x^2} + {4^2}} = \sqrt {{x^2} + 16} \cr
& \cr
& {\text{Express sin}}\theta {\text{ in terms of }}x \cr
& \sin \theta = \frac{{{\text{Opposite side}}}}{{{\text{Hypotenuse}}}} \cr
& \sin \theta = \frac{x}{{\sqrt {{x^2} + 16} }} \cr} $$
