gaokao 2015 Q16

gaokao · China · zhejiang-science Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation
16. (This question is worth 14 points) In $\triangle ABC$, the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given that $A = \frac { \pi } { 4 }$ and $b ^ { 2 } - a ^ { 2 } = \frac { 1 } { 2 } c ^ { 2 }$ . (I) Find the value of $\tan C$; (II) If the area of $\triangle ABC$ is 7, find the value of $b$. 
16. (This question is worth 14 points)\\
In $\triangle ABC$, the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given that $A = \frac { \pi } { 4 }$ and $b ^ { 2 } - a ^ { 2 } = \frac { 1 } { 2 } c ^ { 2 }$ .\\
(I) Find the value of $\tan C$;\\
(II) If the area of $\triangle ABC$ is 7, find the value of $b$.
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