Решебник по геометрии 9 класс Мерзляк Задание 39

\[a = 3\ см;\ \ \ b = 4\ см;\ \ \ \]

\[\sin{\angle c} = \frac{\sqrt{35}}{6}.\]

\[1)\ \cos{\angle c} = \pm \sqrt{1 - \sin^{2}{\angle c}} =\]

\[= \pm \sqrt{1 - \frac{35}{36}} = \pm \sqrt{\frac{1}{36}} = \pm \frac{1}{6}.\]

\[2)\ \cos{\angle c} = - \frac{1}{6}:\]

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

\[= 9 + 16 - 2 \bullet 3 \bullet 4 \bullet \left( - \frac{1}{6} \right) =\]

\[= 25 + 4 = 29;\]

\[c = \sqrt{29}\ см.\]

\[3)\ \cos{\angle c} = \frac{1}{6}:\]

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

\[= 9 + 16 - 2 \bullet 3 \bullet 4 \bullet \frac{1}{6} =\]

\[= 25 - 4 = 21;\]

\[c = \sqrt{21}\ см.\]

\[Ответ:\ \ \sqrt{21}\ см;\ \sqrt{29}\ см.\]