gaokao 2015 Q13

gaokao · China · chongqing-arts 5 marks Sine and Cosine Rules Find a side length using the cosine rule
In $\triangle A B C$, let the sides opposite to angles $\mathrm { A } , \mathrm { B } , \mathrm { C }$ be $a , b , c$ respectively. Given $a = 2 , \cos C = - \frac { 1 } { 4 } , 3 \sin A = 2 \sin B$, then $\mathrm { c } =$ $\_\_\_\_$ .
In $\triangle A B C$, let the sides opposite to angles $\mathrm { A } , \mathrm { B } , \mathrm { C }$ be $a , b , c$ respectively. Given $a = 2 , \cos C = - \frac { 1 } { 4 } , 3 \sin A = 2 \sin B$, then $\mathrm { c } =$ $\_\_\_\_$ .