Решебник по геометрии 9 класс Мерзляк Задание 28

\[1)\ AB = 5\ см;\ BC = 8\ см;\ \]

\[\angle B = 60{^\circ}:\]

\[AC^{2} =\]

\[= AB^{2} + BC^{2} - 2AB \bullet BC \bullet \cos{\angle B} =\]

\[= 25 + 64 - 2 \bullet 5 \bullet 8 \bullet \cos{60{^\circ}} =\]

\[= 89 - 80 \bullet \frac{1}{2} = 89 - 40 = 49;\]

\[AC = \sqrt{49} = 7\ см.\]

\[Ответ:\ \ 7\ см.\]

\[2)\ AB = 3\ см;\ AC = 2\sqrt{2}\ см;\ \ \ \]

\[\angle A = 135{^\circ}:\]

\[BC^{2} =\]

\[= AB^{2} + AC^{2} - 2AB \bullet AC \bullet \cos{\angle A} =\]

\[= 9 + 8 - 2 \bullet 3 \bullet 2\sqrt{2} \bullet \cos{135{^\circ}} =\]

\[= 17 + 12\sqrt{2} \bullet \frac{\sqrt{2}}{2} =\]

\[= 17 + 12 = 29;\]

\[BC = \sqrt{29}\ см.\]

\[Ответ:\ \ \sqrt{29}\ см.\]