Решебник по геометрии 9 класс Мерзляк Задание 78

\[Рисунок\ в\ учебнике.\]

\[Дано:\]

\[AC = 4\sqrt{2};\]

\[\angle A = 60{^\circ};\]

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

\[Найти:\]

\[\text{BC.}\]

\[Решение.\]

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

\[BC = \frac{AC \bullet \sin{\angle A}}{\sin{\angle B}}\]

\[BC = 4\sqrt{2} \bullet \frac{\sin{60{^\circ}}}{\sin{45{^\circ}}}\]

\[BC = 4\sqrt{2} \bullet \frac{\sqrt{3}}{2}\ :\frac{\sqrt{2}}{2} =\]

\[= \frac{4\sqrt{2} \bullet \sqrt{3}}{\sqrt{2}} = 4\sqrt{3}\ см.\]

\[Ответ:\ \ 4\sqrt{3}\ см.\]