gaokao 2023 Q18

gaokao · China · national-B-science 12 marks Sine and Cosine Rules Multi-step composite figure problem
In $\triangle A B C$, it is given that $\angle B A C = 120 ^ { \circ } , A B = 2 , A C = 1$.
(1) Find $\sin \angle A B C$.
(2) If $D$ is a point on $BC$ such that $\angle B A D = 90 ^ { \circ }$, find the area of $\triangle A D C$.
In $\triangle A B C$, it is given that $\angle B A C = 120 ^ { \circ } , A B = 2 , A C = 1$.\\
(1) Find $\sin \angle A B C$.\\
(2) If $D$ is a point on $BC$ such that $\angle B A D = 90 ^ { \circ }$, find the area of $\triangle A D C$.