Решебник по геометрии 9 класс Мерзляк Задание 116

\[1)\ a = 10\ см,\ \beta = 20{^\circ},\ \gamma = 85{^\circ}:\]

\[\alpha = 180{^\circ} - 20{^\circ} - 85{^\circ} = 75{^\circ};\]

\[b = \frac{a\sin\beta}{\sin\alpha} = \frac{10 \bullet \sin{20{^\circ}}}{\sin{75{^\circ}}} \approx 3,5\ см;\]

\[c = \frac{a\sin\gamma}{\sin\alpha} = \frac{10 \bullet \sin{85{^\circ}}}{\sin{75{^\circ}}} \approx 10,3\ см.\]

\[2)\ b = 16\ см,\ \alpha = 40{^\circ},\ \beta = 110{^\circ}:\]

\[\gamma = 180{^\circ} - 40{^\circ} - 110{^\circ} = 30{^\circ};\]

\[a = \frac{b\sin\alpha}{\sin\beta} = \frac{16 \bullet \sin{40{^\circ}}}{\sin{110{^\circ}}} \approx\]

\[\approx 10,9\ см;\]

\[c = \frac{b\sin\gamma}{\sin\beta} = \frac{16 \bullet \sin{30{^\circ}}}{\sin{110{^\circ}}} \approx\]

\[\approx 8,5\ см.\]