$6-$ The structure shown below has five simply supported cables pinned to a rigid ceiling and laid symmetrically with respect to the middle cable $($cable $1).$ The angle between cables $2,4$ and the ceiling is $70$ degrees and between cables $3,5$ and the ceiling is $50$ degrees. Using Castigliano's first theorem, determine the forces in the $5$ cables due to a force P of $10$ KN applied at the common joint of all five cables as shown. Assume all cables have the same cross sectional area $\backslash (\backslash$mathrm$\{$A$\}=200\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ and $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ).$ Also take the length of cable $\backslash (1,\backslash$mathrm$\{$~L$\}\_\{1\}=\backslash )2000$ mm $.$