回復 1# thankyou 的帖子
\(\begin{align}
& \Delta ABC=\frac{1}{2}\times \overline{AC}\times \overline{BC} \\
& \Delta ABC=\Delta AOC+\Delta BOC \\
& =\frac{1}{2}\times \overline{OC}\times \overline{OA}\times \sin \angle AOC+\frac{1}{2}\times \overline{OC}\times \overline{OB}\times \sin \angle BOC \\
& =\frac{1}{2}\times \overline{OC}\times \overline{OC}\times \sin \angle AOC+\frac{1}{2}\times \overline{OC}\times \overline{OC}\times \sin \angle AOC \\
& ={{\overline{OC}}^{2}}\times \sin \angle AOC \\
& \\
& \sin \angle AOC=\frac{1}{2} \\
& \angle AOC={{30}^{{}^\circ }}\ or\ {{150}^{{}^\circ }} \\
& \angle CAB={{15}^{{}^\circ }}\ or\ {{75}^{{}^\circ }} \\
\end{align}\)