Решебник по геометрии 9 класс Мерзляк Задание 120

\[1)\ a = 4\ см,\ \ \ b = 5\ см,\ \ \ c = 7\ см:\]

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

\[= \frac{25 + 49 - 16}{2 \bullet 5 \bullet 7};\]

\[\cos\alpha = \frac{58}{70} \approx 0,8286;\ \ \ \]

\[\alpha \approx 34{^\circ}.\]

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

\[= \frac{16 + 49 - 25}{2 \bullet 4 \bullet 7} = \frac{40}{56} \approx 0,7143;\]

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

\[\gamma = 180{^\circ} - 34{^\circ} - 44{^\circ} = 102{^\circ}.\]

\[2)\ a = 26\ см,\ b = 19\ см,\ c = 42\ см;\]

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

\[= \frac{361 + 1764 - 676}{2 \bullet 19 \bullet 42} =\]

\[= \frac{1449}{1596} \approx 0,9079;\ \ \]

\[\alpha \approx 25{^\circ};\]

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

\[= \frac{676 + 1764 - 361}{2 \bullet 26 \bullet 42} =\]

\[= \frac{2079}{2184} \approx 0,9519;\ \ \]

\[\beta \approx 18{^\circ};\]

\[\gamma = 180{^\circ} - 25{^\circ} - 18{^\circ} = 137{^\circ}.\]