ГДЗ по геометрии 9 класс Мерзляк Задание 91

\[Схематический\ рисунок.\]

\[Дано:\]

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

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

\[\angle ADC = 45{^\circ};\]

\[R_{\mathrm{\Delta}ABC} = 4\ см.\]

\[Найти:\]

\[R_{\mathrm{\Delta}ACD}.\]

\[Решение.\]

\[1)\ В\ \mathrm{\Delta}ABC:\]

\[R = \frac{\text{AC}}{2\sin{\angle B}}\text{\ \ \ }\]

\[AC = 2R\sin{\angle B} =\]

\[= 2 \bullet 4 \bullet \sin{60{^\circ}} = 8 \bullet \frac{\sqrt{3}}{2} = 4\sqrt{3}.\]

\[2)\ В\ \mathrm{\Delta}\text{ACD}\]

\[R = \frac{\text{AC}}{2\sin{\angle D}} = \frac{4\sqrt{3}}{2\sin{45{^\circ}}} =\]

\[= 2\sqrt{3}\ :\frac{\sqrt{2}}{2} = 2\sqrt{3} \bullet \sqrt{2} = 2\sqrt{6}\ см.\]

\[Ответ:\ \ 2\sqrt{6}\ см.\]