[tex]\it tgB=tg60^o=\sqrt3\ \ \ \ \ (1)\\ \\ \\ tgB=\dfrac{AC}{AB}=\dfrac{6}{AB} \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \dfrac{6}{AB}=\sqrt3 \Rightarrow AB=\dfrac{^{\sqrt3)}6}{\ \ \sqrt3}=\dfrac{6\sqrt3}{3}=2\sqrt3[/tex]
[tex]\it \mathcal{A}=\dfrac{c_1\cdot c_2}{2}=\dfrac{AB\cdot AC}{2}=\dfrac{2\sqrt3\cdot6}{2}=6\sqrt3\ cm^2[/tex]
