Решебник по геометрии 9 класс Мерзляк Задание 80

\[Дано:\]

\[\mathrm{\Delta}ABC;\]

\[AC = \sqrt{6}\ см;\]

\[\angle B = 120{^\circ};\]

\[\angle C = 45{^\circ}.\]

\[Найти:\]

\[\text{AB.}\]

\[Решение.\]

\[\frac{\text{AB}}{\sin{\angle C}} = \frac{\text{AC}}{\sin{\angle B}}\]

\[AB = \frac{AC \bullet \sin{\angle C}}{\sin{\angle B}}\]

\[AB = \sqrt{6} \bullet \frac{\sin{45{^\circ}}}{\sin{120{^\circ}}}\]

\[AB = \sqrt{6} \bullet \frac{\sqrt{2}}{2}\ :\frac{\sqrt{3}}{2} =\]

\[= \frac{\sqrt{6} \bullet \sqrt{2}}{\sqrt{3}} = 2\ см.\]

\[Ответ:\ \ 2\ см.\]