ГДЗ по геометрии 9 класс Мерзляк Задание 118

\[1)\ b = 18\ см,\ c = 22\ см,\ \alpha = 76{^\circ}:\]

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

\[a = \sqrt{324 + 484 - 36 \bullet 22 \bullet \cos{76{^\circ}}};\]

\[a = \sqrt{808 - 792 \bullet 0,24} \approx 24,8\ см;\]

\[\sin\beta = \frac{b\sin\alpha}{a} = \frac{18 \bullet \sin{76{^\circ}}}{24,8};\]

\[\sin\beta \approx 0,7042;\ \ \ \]

\[\beta \approx 45{^\circ};\]

\[\gamma = 180{^\circ} - 76{^\circ} - 45{^\circ} = 59{^\circ}.\]

\[2)\ a = 20\ см,\ b = 15\ см,\ \gamma = 104{^\circ};\]

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

\[c = \sqrt{400 + 225 - 40 \bullet 15 \bullet \cos{104{^\circ}}};\]

\[c = \sqrt{625 + 600 \bullet 0,24} \approx 27,8\ см;\]

\[\sin\alpha = \frac{a\sin\gamma}{c} = \frac{20 \bullet \sin{104{^\circ}}}{27,8};\]

\[\sin\alpha \approx 0,6981;\ \ \ \]

\[\alpha \approx 44{^\circ};\]

\[\beta = 180{^\circ} - 104{^\circ} - 44{^\circ} = 32{^\circ}.\]