\[Дано:\]
\[\mathrm{\Delta}ABC;\]
\[AB = 16\ см;\]
\[BC = 14\ см;\]
\[\angle A = 60{^\circ}.\]
\[Решение.\]
\[196 = 256 + AC^{2} - 2 \bullet 16 \bullet AC \bullet \frac{1}{2}\]
\[AC^{2} - 16AC + 60 = 0\]
\[D = 16^{2} - 4 \bullet 60 = 16\]
\[AC_{1} = \frac{16 - 4}{2} = 6\ см;\text{\ \ }\]
\[AC_{2} = \frac{16 + 4}{2} = 10\ см.\]
\[Ответ:\ \ 6\ см;\ 10\ см.\]