Решебник по геометрии 9 класс Мерзляк Задание 79

\[Рисунок\ в\ учебнике.\]

\[Дано:\]

\[AB = 6\sqrt{2};\]

\[BC = 6;\]

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

\[Найти:\]

\[\angle A.\]

\[Решение.\]

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

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

\[\sin{\angle A} = \frac{6 \bullet \sin{45{^\circ}}}{6\sqrt{2}} =\]

\[= \frac{1}{\sqrt{2}} \bullet \frac{\sqrt{2}}{2} = \frac{1}{2}\]

\[\angle A = \arcsin\frac{1}{2} = 30{^\circ}.\]

\[Ответ:\ \ 30{^\circ}.\]