gaokao 2015 Q13

gaokao · China · chongqing-science Sine and Cosine Rules Multi-step composite figure problem
13. In $\triangle \mathrm { ABC }$, $\mathrm { B } = 120 ^ { \circ } , \mathrm { AB } = \sqrt { 2 }$, and the angle bisector from $A$ is $\mathrm { AD } = \sqrt { 3 }$, then $\mathrm { AC } = $ $\_\_\_\_$ . Note for Candidates: Questions (14), (15), and (16) are optional. Please choose any two to answer. If all three are answered, only the first two will be graded.
13. In $\triangle \mathrm { ABC }$, $\mathrm { B } = 120 ^ { \circ } , \mathrm { AB } = \sqrt { 2 }$, and the angle bisector from $A$ is $\mathrm { AD } = \sqrt { 3 }$, then $\mathrm { AC } = $ $\_\_\_\_$ .\\
Note for Candidates: Questions (14), (15), and (16) are optional. Please choose any two to answer. If all three are answered, only the first two will be graded.\\