For an angle $\displaystyle\theta\usepackage{cmbright}\Huge\$ in standard position, with the terminal side intersecting the unit circle at the point $\displaystyle{\left({x},{y}\right)}\usepackage{cmbright}\Huge\$ , the value of the tangent function is given by $\displaystyle{\tan{\theta}}=\frac{{y}}{{x}}\usepackage{cmbright}\Huge\$ . Therefore:

$\displaystyle{{\tan{{30}}}}^{\circ}=\frac{{\frac{{1}}{{2}}}}{{\frac{\sqrt{{3}}}{{2}}}}=\frac{{1}}{{2}}\cdot\frac{{2}}{\sqrt{{3}}}=\frac{{1}}{\sqrt{{3}}}=\frac{{1}}{\sqrt{{3}}}\cdot\frac{\sqrt{{3}}}{\sqrt{{3}}}=\frac{\sqrt{{3}}}{{3}}\usepackage{cmbright}\Huge\$