gaokao 2015 Q16

gaokao · China · tianjin-arts 13 marks Sine and Cosine Rules Find a side length using the cosine rule
16. (13 points) In $\triangle ABC$, the sides opposite to angles $A, B, C$ are $a, b, c$ respectively. Given that the area of $\triangle ABC$ is $3 \sqrt { 15 }$, $b - c = 2$, $\cos A = - \frac { 1 } { 4 }$. (I) Find the values of $a$ and $\sin C$; (II) Find the value of $\cos \left( 2 A + \frac { \pi } { 6 } \right)$. 
16. (13 points) In $\triangle ABC$, the sides opposite to angles $A, B, C$ are $a, b, c$ respectively. Given that the area of $\triangle ABC$ is $3 \sqrt { 15 }$, $b - c = 2$, $\cos A = - \frac { 1 } { 4 }$.\\
(I) Find the values of $a$ and $\sin C$;\\
(II) Find the value of $\cos \left( 2 A + \frac { \pi } { 6 } \right)$.\\
Paper Questions
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