Since TSQ and QSR are supplementary, they give 180 when summed. TSQ is 150, so QSR must be 30.
Therefore, you have
[tex]\tan(30)=\dfrac{\sin(30)}{\cos(30)}=\dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \dfrac{1}{2}\cdot\dfrac{2}{\sqrt{3}}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]
