Решебник по геометрии 9 класс Мерзляк Задание 101

\[Схематический\ рисунок.\]

\[Дано:\]

\[BC = 1\ ч;\]

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

\[\angle C = 50{^\circ}.\]

\[Найти:\]

\[P_{\text{ABC}}.\]

\[Решение.\]

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

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

\[\frac{1}{\sin{30{^\circ}}} = \frac{\text{AB}}{\sin{50{^\circ}}} = \frac{\text{AC}}{\sin{100{^\circ}}}\]

\[\frac{\text{AB}}{0,76} = \frac{\text{AC}}{0,98} = 2\]

\[AB \approx 1,52;\ \ AC \approx 1,96.\]

\[P_{\text{ABC}} = AB + BC + AC =\]

\[= 1,52 + 1 + 1,96 \approx 4,5\ ч.\]

\[Ответ:\ \ 4,5\ ч.\]