Решебник по геометрии 9 класс Мерзляк Задание 119

\[1)\ a = 8\ см,\ \ \ c = 6\ см,\ \ \ \beta = 15{^\circ}:\]

\[b = \sqrt{a^{2} + c^{2} - 2ac \bullet \cos\beta};\]

\[b = \sqrt{64 + 36 - 2 \bullet 8 \bullet 6 \bullet \cos{15{^\circ}}};\]

\[b = \sqrt{100 - 96 \bullet 0,97} \approx 2,7\ см;\]

\[\sin\alpha = \frac{a\sin\beta}{b} = \frac{8 \bullet \sin{15{^\circ}}}{2,7};\]

\[\sin\alpha \approx 0,7669;\ \ \]

\[\alpha \approx 130{^\circ};\]

\[\gamma = 180{^\circ} - 15{^\circ} - 130{^\circ} = 35{^\circ}.\]

\[2)\ b = 7\ см,\ c = 5\ см,\ \alpha = 145{^\circ}:\]

\[a = \sqrt{b^{2} + c^{2} - 2bc \bullet \cos\alpha};\]

\[a = \sqrt{49 + 25 - 14 \bullet 5 \bullet \cos{145{^\circ}}};\]

\[a = \sqrt{74 + 70 \bullet 0,82} \approx 11,5\ см;\]

\[\sin\beta = \frac{b\sin\alpha}{a} = \frac{7 \bullet \sin{145{^\circ}}}{11,5};\]

\[\sin\beta \approx 0,3491;\ \ \ \]

\[\beta \approx 20{^\circ};\]

\[\gamma = 180{^\circ} - 145{^\circ} - 20{^\circ} = 15{^\circ}.\]