ГДЗ по геометрии 9 класс Мерзляк Задание 111

\[Рисунок\ в\ учебнике.\]

\[Дано:\]

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

\[\angle A = 30{^\circ};\]

\[\angle B = 70{^\circ};\]

\[AB = a.\]

\[Найти:\]

\[AC;\ BC.\]

\[Решение.\]

\[1)\ В\ \mathrm{\Delta}ABC:\]

\[\angle C = 180{^\circ} - \angle A - \angle B = 80{^\circ};\]

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

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

\[= a \bullet \frac{\sin{70{^\circ}}}{\sin{80{^\circ}}} \approx 0,9542a;\]

\[BC = \frac{AB \bullet \sin{\angle A}}{\sin{\angle C}} =\]

\[= a \bullet \frac{\sin{30{^\circ}}}{\sin{80{^\circ}}} \approx 0,5077a.\]

\[2)\ Время\ в\ пути:\]

\[AC = \frac{0,9542a}{90} \approx 0,0106a;\]

\[BC = \frac{0,5077a}{60} \approx 0,0085a.\]

\[Ответ:\ \ автобус.\]