Решебник по геометрии 9 класс Мерзляк Задание 100

\[Дано:\]

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

\[AB = 24\ см;\]

\[R_{опис} = 8\sqrt{3}\ см.\]

\[Найти:\]

\[\angle C.\]

\[Решение.\]

\[R = \frac{\text{AB}}{2\sin{\angle C}}\text{\ \ \ }\]

\[\sin{\angle C} = \frac{\text{AB}}{2R}\]

\[\sin{\angle C} = \frac{24}{2 \bullet 8\sqrt{3}} = \frac{3}{2\sqrt{3}} = \frac{\sqrt{3}}{2}.\]

\[\angle C = \arcsin\frac{\sqrt{3}}{2} = 60{^\circ}\]

\[\angle C = 180{^\circ} - 60{^\circ} = 120.\]

\[Ответ:\ \ 60{^\circ};\ 120{^\circ}.\]