Решебник по геометрии 9 класс Мерзляк Задание 135

\[1)\ AB = 12\ см;\ \ \]

\[BC = 10\ см;\ \ \ \]

\[S_{\text{ABC}} = 30\sqrt{3}\ см^{2}:\]

\[S_{\text{ABC}} = \frac{1}{2}AB \bullet BC \bullet \sin{\angle B}\]

\[12 \bullet 10 \bullet \sin{\angle B} = 60\sqrt{3}\text{\ \ \ }\]

\[\sin{\angle B} = \frac{\sqrt{3}}{2}\text{\ \ }\]

\[\angle B = 60{^\circ}.\]

\[Ответ:\ \ 60{^\circ};\ 120{^\circ}.\]

\[2)\ AB = 14\ см;\ \ \]

\[AC = 8\ см;\ \ \ \]

\[S_{\text{ABC}} = 56\ см^{2}:\]

\[S_{\text{ABC}} = \frac{1}{2}AB \bullet AC \bullet \sin{\angle A}\]

\[14 \bullet 8 \bullet \sin{\angle A} = 112\ \ \]

\[\sin{\angle A} = 1\ \ \ \]

\[\angle A = 90{^\circ}.\]

\[Ответ:\ \ 90{^\circ}.\]