$\begin{align}  & \cos C=\frac{{{c}^{2}}-{{a}^{2}}-{{b}^{2}}}{-2ab} \\ & \cos C=\frac{{{\left( \sqrt{3}t \right)}^{2}}-{{t}^{2}}-{{t}^{2}}}{-2(t)(t)} \\ & \cos C=\frac{3{{t}^{2}}-2{{t}^{2}}}{-2{{t}^{2}}}=\frac{{{t}^{2}}}{2{{t}^{2}}}=\frac{1}{2} \\ & C={{\cos }^{-1}}(-\tfrac{1}{2})=-{{60}^{o}}={{180}^{\circ }}-{{60}^{\circ }}={{120}^{\circ }} \\\end{align}$