Решебник по геометрии 9 класс Мерзляк Задание 117

\[1)\ b = 9\ см,\ \ \ \alpha = 35{^\circ},\ \ \ \gamma = 70{^\circ}:\]

\[\beta = 180{^\circ} - 35{^\circ} - 70{^\circ} = 75{^\circ};\]

\[a = \frac{b\sin\alpha}{\sin\beta} = \frac{9 \bullet \sin{35{^\circ}}}{\sin{75{^\circ}}} \approx 5,3\ см;\]

\[c = \frac{b\sin\gamma}{\sin\beta} = \frac{9 \bullet \sin{70{^\circ}}}{\sin{75{^\circ}}} \approx 8,8\ см.\]

\[2)\ c = 14\ см,\ \ \ \beta = 132{^\circ},\ \ \ \gamma = 24{^\circ}:\]

\[\alpha = 180{^\circ} - 132{^\circ} - 24{^\circ} = 24{^\circ};\]

\[a = \frac{c\sin\alpha}{\sin\gamma} = \frac{14 \bullet \sin{24{^\circ}}}{\sin{24{^\circ}}} = 14\ см;\]

\[b = \frac{c\sin\beta}{\sin\gamma} =\]

\[= \frac{14 \bullet \sin{132{^\circ}}}{\sin{24{^\circ}}} \approx 25,6\ см.\]