gaokao 2020 Q18

gaokao · China · national-I-arts 12 marks Sine and Cosine Rules Compute area of a triangle or related figure
In $\triangle A B C$, the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given $B = 150 ^ { \circ }$ ,
(1) If $a = \sqrt { 3 } c , b = 2 \sqrt { 7 }$ , find the area of $\triangle A B C$ ;
(2) If $\sin A + \sqrt { 3 } \sin C = \frac { \sqrt { 2 } } { 2 }$ , find $C$ .
In $\triangle A B C$, the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given $B = 150 ^ { \circ }$ ,

(1) If $a = \sqrt { 3 } c , b = 2 \sqrt { 7 }$ , find the area of $\triangle A B C$ ;

(2) If $\sin A + \sqrt { 3 } \sin C = \frac { \sqrt { 2 } } { 2 }$ , find $C$ .