Решебник по геометрии 9 класс Мерзляк Задание 265

\[Схематический\ рисунок.\]

\[Дано:\]

\[AB = 6\ см;\]

\[\angle A = 50{^\circ};\]

\[\angle B = 100{^\circ}.\]

\[Найти:\]

\[\cup AB;\ \]

\[\cup BC;\]

\[\cup AC.\]

\[Решение.\]

\[1)\ В\ \mathrm{\Delta}ABC:\]

\[\angle C = 180{^\circ} - \angle A - \angle B = 30{^\circ};\]

\[R = \frac{\text{AB}}{2\sin{\angle C}} = \frac{6}{2\sin{30{^\circ}}} = 6.\]

\[2)\ Окружность:\]

\[C = 2\pi R = 2\pi \bullet 6 = 12\pi;\]

\[\cup AB = 2 \bullet 12\pi \bullet \frac{30{^\circ}}{360{^\circ}} = 2\pi;\]

\[\cup BC = 2 \bullet 12\pi \bullet \frac{50{^\circ}}{360{^\circ}} = \frac{10\pi}{3};\]

\[\cup AC = 2 \bullet 12\pi \bullet \frac{100{^\circ}}{360{^\circ}} = \frac{20\pi}{3}.\]

\[Ответ:\ \ 2\pi\ см;\ \frac{10\pi}{3}\ см;\ \frac{20\pi}{3}\ см.\]