Решебник по геометрии 9 класс Мерзляк Задание 123

\[1)\ a = 7\ см,\ b = 11\ см,\ \beta = 46{^\circ}:\]

\[\sin\alpha = \frac{a\sin\beta}{b} = \frac{7 \bullet \sin{46{^\circ}}}{11};\]

\[\sin\alpha \approx 0,4578;\ \ \ \]

\[\alpha \approx 27{^\circ};\]

\[\gamma = 180{^\circ} - 27{^\circ} - 46{^\circ} = 107{^\circ};\]

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

\[= \frac{11 \bullet \sin{107{^\circ}}}{\sin{46{^\circ}}} \approx 14,6\ см.\]

\[2)\ b = 15\ см,\ c = 17\ см,\ \beta = 32{^\circ}:\]

\[\sin\gamma = \frac{c\sin\beta}{b} = \frac{17 \bullet \sin{32{^\circ}}}{15};\]

\[\sin\gamma \approx 0,6006.\ \]

\[\gamma_{1} \approx 37{^\circ};\ \ \ \gamma_{2} \approx 143{^\circ}:\]

\[\alpha_{1} = 180{^\circ} - 32{^\circ} - 37{^\circ} = 111{^\circ};\]

\[a_{1} = \frac{c\sin\alpha}{\sin\gamma} =\]

\[= \frac{17 \bullet \sin{111{^\circ}}}{\sin{37{^\circ}}} \approx 26,4\ см;\]

\[\alpha_{2} = 180{^\circ} - 32{^\circ} - 143{^\circ} = 5{^\circ};\]

\[a_{2} = \frac{c\sin\alpha}{\sin\gamma} = \frac{17 \bullet \sin{5{^\circ}}}{\sin{143{^\circ}}} \approx 2,5\ см.\]

\[3)\ a = 7\ см,\ \ \ c = 3\ см,\ \ \ \gamma = 27{^\circ}:\]

\[\sin\alpha = \frac{a\sin\gamma}{c} = \frac{7 \bullet \sin{27{^\circ}}}{3};\]

\[\sin\alpha \approx 1,0593;\ \]

\[\ \alpha - не\ существует.\]