Correct. The acute angles are complementary, so $\displaystyle{m}\angle{S}={{30}}^{\circ}\usepackage{cmbright}\Huge\$ . This is a $\displaystyle{{30}}^{\circ}-{{60}}^{\circ}-{{90}}^{\circ}\usepackage{cmbright}\Huge\$ triangle. One way to find the length of the hypotenuse is to use the sine function, because you know the value of $\displaystyle{{\sin{{60}}}}^{\circ}\usepackage{cmbright}\Huge\$ :

$\displaystyle\frac{{{5}\sqrt{{3}}}}{{t}}={{\sin{{60}}}}^{\circ}=\frac{\sqrt{{3}}}{{2}}\Rightarrow{10}\sqrt{{3}}={t}\sqrt{{3}}\Rightarrow{10}={t}\usepackage{cmbright}\Huge\$

One way to find the length of $\displaystyle{\overline{{{R}{T}}}}\usepackage{cmbright}\Huge\$ is to use the tangent function:

$\displaystyle\frac{{{5}\sqrt{{3}}}}{{s}}={{\tan{{60}}}}^{\circ}=\sqrt{{3}}\Rightarrow{5}\sqrt{{3}}={s}\sqrt{{3}}\Rightarrow{5}={s}\usepackage{cmbright}\Huge\$