\[\boxed{\mathbf{1032.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Рисунок\ по\ условию\ задачи:\]
\[\mathbf{Дано:}\]
\[\overrightarrow{F_{1}} = \overrightarrow{F_{2}};\]
\[\angle F_{1}AF_{2} = 72{^\circ};\]
\[\left| \overrightarrow{F} \right| = 120\ кг.\]
\[\mathbf{Найти:}\]
\[\left| \overrightarrow{F_{1}} \right|;\left| \overrightarrow{F_{2}} \right| - ?\]
\[\mathbf{Решение.}\]
\[1)\ В\ \mathrm{\Delta}AA_{1}F_{2}:\]
\[\angle A_{1} = 90{^\circ};\ \angle AF_{2}A_{1} = 72{^\circ} \Longrightarrow\]
\[\Longrightarrow AA_{1} = AF_{2} \bullet \sin{72{^\circ}}.\]
\[2)\ AF_{1}FF_{2} - ромб\ \]
\[(по\ построению).\]
\[3)\ В\ \mathrm{\Delta}AA_{1}F:\]
\[\angle A_{1} = 90{^\circ};\ \]
\[\angle AFA_{1} = 36{^\circ} \Longrightarrow\]
\[\Longrightarrow \ AA_{1} = AF \bullet \sin{36{^\circ}}.\]
\[4)\ AF_{2} \bullet \sin{72{^\circ}} = AF \bullet \sin{36{^\circ}}\]
\[AF_{2} \bullet \sin{72{^\circ}} = 120 \bullet \sin{36{^\circ}}\]
\[AF_{2} = \frac{120 \bullet 0,5878}{0,9511} = 74,2\ кг.\]
\[5)\ AF_{2} = AF_{1} = 74,2\ кг.\]
\[\mathbf{Ответ:}\left| \overrightarrow{F_{1}} \right| = \left| \overrightarrow{F_{2}} \right| = 74,2\ к\mathbf{г}\mathbf{.}\]