$1)10$ The cable running from $\backslash ($ D $\backslash )$ to $\backslash ($ C $\backslash )$ is running through a frictionless pulley at $\backslash ($ B $\backslash ).$ the cable running from $\backslash ($ A $\backslash )$ to $\backslash ($ B $\backslash )$ is fixed at $\backslash ($ B $\backslash )$ and has unknown tension. The tension at $\backslash ($ C $\backslash )$ is $1000$ N $.$

What is the tension in the cable that is fixed to $\backslash ($ B $\backslash )$ and is running to $\backslash ($ A $\backslash ),$ and what is the angle between the horizontal and the cable running $\backslash ($ B $\backslash )$ to $\backslash (\backslash$underline$\{\backslash$underline$\{$D$\}\}\backslash )?$

Provide a free body diagram, the equilibrium equations, and solution.