gaokao 2024 Q15

gaokao · China · national-I_github 13 marks Sine and Cosine Rules Determine an angle or side from a trigonometric identity/equation
(13 points) Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively. Given $\sin C = \sqrt { 2 } \cos B , a ^ { 2 } + b ^ { 2 } - c ^ { 2 } = \sqrt { 2 } a b$ .
(1) Find $B$ ;
(2) If the area of $\triangle A B C$ is $3 + \sqrt { 3 }$ , find $c$ .
(13 points)\\
Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively. Given $\sin C = \sqrt { 2 } \cos B , a ^ { 2 } + b ^ { 2 } - c ^ { 2 } = \sqrt { 2 } a b$ .\\
(1) Find $B$ ;\\
(2) If the area of $\triangle A B C$ is $3 + \sqrt { 3 }$ , find $c$ .