Решебник по геометрии 9 класс Мерзляк Задание 121

\[1)\ a = 5\ см,\ b = 6\ см,\ c = 8\ см:\]

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

\[= \frac{36 + 64 - 25}{2 \bullet 6 \bullet 8}\frac{75}{96} \approx 0,7813;\]

\[\alpha \approx 39{^\circ};\]

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

\[= \frac{25 + 64 - 36}{2 \bullet 5 \bullet 8} = \frac{53}{80} \approx 0,6625;\]

\[\beta \approx 49{^\circ};\]

\[\gamma = 180{^\circ} - 39{^\circ} - 49{^\circ} = 92{^\circ}.\]

\[2)\ a = 21\ см,\ b = 17\ см,\ c = 32\ см;\]

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

\[= \frac{289 + 1024 - 441}{2 \bullet 17 \bullet 32} =\]

\[= \frac{872}{1088} \approx 0,8015;\]

\[\alpha \approx 37{^\circ};\]

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

\[= \frac{441 + 1024 - 289}{2 \bullet 21 \bullet 32} =\]

\[= \frac{1176}{1344} \approx 0,8750;\]

\[\beta \approx 29{^\circ}.\]

\[\gamma = 180{^\circ} - 37{^\circ} - 29{^\circ} = 114{^\circ}.\]