Решебник по геометрии 9 класс Мерзляк Задание 122

\[1)\ a = 10\ см,\ b = 3\ см,\ \beta = 10{^\circ}:\]

\[\sin\alpha = \frac{a\sin\beta}{b} = \frac{10 \bullet \sin{10{^\circ}}}{3};\]

\[\sin\alpha \approx 0,5789;\ \ \ \]

\[\alpha \approx 35{^\circ};\]

\[\gamma = 180{^\circ} - 35{^\circ} - 10{^\circ} = 135{^\circ};\]

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

\[= \frac{3 \bullet \sin{135{^\circ}}}{\sin{10{^\circ}}} \approx 12,2\ см.\]

\[2)\ a = 10\ см,\ b = 3\ см,\ \beta = 10{^\circ}:\]

\[\sin\alpha = \frac{a\sin\beta}{b} = \frac{10 \bullet \sin{10{^\circ}}}{3};\]

\[\sin\alpha \approx 0,5789;\ \ \]

\[\alpha \approx 145{^\circ};\]

\[\gamma = 180{^\circ} - 145{^\circ} - 10{^\circ} = 25{^\circ};\]

\[c = \frac{b\sin\gamma}{\sin\beta} = \frac{3 \bullet \sin{25{^\circ}}}{\sin{10{^\circ}}} \approx 7,3\ см.\]