(Solved): Please and Thank You Rope \( B C A \) passes through a pulley at point \( C \) and supports a crate ...

Rope \( B C A \) passes through a pulley at point \( C \) and supports a crate at point \( A \). Rope segment \( C D \) supports the pulley and is attached to an eye anchor embedded in a wall. Rope segment \( B C \) creates an angle of \( \phi=59.0^{\circ} \) with the floor and rope segment \( C D \) creates an angle \( \theta \) with the horizontal. If both ropes \( B C A \) and \( C D \) can support a maximum tensile force \( T_{\max }=170 \mathrm{lb} \), what is the maximum weight \( W_{\max } \) of the crate that the system can support? What is the angle \( \theta \) required for equilibrium? Express your answers numerically in pounds and degrees to three significant figures separated by a comma. View Available Hint(s) Leatming Goal: To understand how to establish a particle's free-body diagram in a coplanar force system and to apply the equations of epulibrium to solve for unlinowns In a coplanar force system, a particle is subjected to forces that le in a single plane. If that plane is the \( x-y \) plane, then the cond sens of equinbridin are trit when For this vector equation to be natisfled, the force vector's \( x \) and \( y \) components must be equal to zero \[ \begin{array}{l} \sum F_{i}=0 \\ \sum F_{v}=0 \end{array} \]