\[\boxed{\mathbf{592.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\textbf{а)}\ tg\ \alpha = \frac{1}{2}:\ \ \ \]
\[tg\ \alpha = \frac{\text{BC}}{\text{AC}} = \frac{1}{2}\]
\[BC = 1;\ AC = 2.\]
\[\textbf{б)}\ tg\ \alpha = \frac{3}{4}:\ \ \ \]
\[tg\ \alpha = \frac{\text{BC}}{\text{AC}} = \frac{3}{4}\]
\[BC = 3;\ AC = 4.\]
\[\textbf{в)}\cos\alpha = \frac{2}{10}:\]
\[\cos\alpha = \frac{\text{AC}}{\text{AB}} = \frac{1}{5}\]
\[AC = 1;\ AB = 5.\]
\[\textbf{г)}\cos\alpha = \frac{2}{3}:\]
\[\cos\alpha = \frac{\text{AC}}{\text{AB}} = \frac{2}{3}\]
\[\ AC = 2;\ AB = 3.\]
\[\textbf{д)}\sin\alpha = \frac{1}{2}:\]
\[\sin\alpha = \frac{\text{BC}}{\text{AB}} = \frac{1}{2}\]
\[BC = 1;\ AB = 2.\]
\[\textbf{е)}\sin\alpha = \frac{4}{10}:\ \ \]
\[\sin\alpha = \frac{\text{BC}}{\text{AB}} = \frac{2}{5}\]
\[BC = 2;\ AB = 5.\]
\[\boxed{\mathbf{592.еуроки - ответы\ на\ пятёрку}}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[ABCD - ромб;\]
\[AB = 10\ см;\]
\[AC = 12\ см.\]
\[\mathbf{Найти:}\]
\[S_{\text{ABCD}} - ?\]
\[DB - ?\]
\[\mathbf{Решение.}\]
\[1)\ По\ свойству\ ромба:\]
\[DO = OB;\]
\[AO = OC = \frac{\text{AC}}{2} = 6\ см.\]
\[2)\ AC\bot DB \Longrightarrow ⊿AOB -\]
\[прямоугольный.\]
\[3)\ По\ теореме\ Пифагора:\ \]
\[OB^{2} = AB^{2} - AO^{2}\]
\[OB^{2} = 100 - 36 = 64\]
\[OB = 8\ см.\]
\[DB = OB \bullet 2 = 16\ см.\]
\[4)\ S_{\text{ABCD}} = \frac{1}{2} \bullet AC \bullet BD =\]
\[= \frac{1}{2} \bullet 16 \bullet 12 = 96\ см^{2}.\]
\[\mathbf{Ответ}:S_{\text{ABCD}} = 96\ см^{2};\]
\[DB = 16\ см\mathbf{.}\]