Problem #$2$: $(25$ points$)$ A weight $W_1=150lb$ and weight $W_2$ are supported by three cables $BA,BC,$ and $CD,$ as seen in the vertical plane shown in Figure $2.$ The locations of points $A,B,C,$ and $D$ are all described by the dimensions given on the figure.

a$)$ Find both the tension $T_{BA}$ in cable $BA$ and the tension $T_{BC}$ in cable $BC.$ Draw the appropriate free body diagram$($s$)$ and label all the relevant forces and angles.

b$)$ Find the tension $T_{CD}$ in cable $CD$ and the weight $W_2.$ Draw the appropriate free body diagram$($s$)$ and label all the relevant forces and angles. SHOW ALL STEPS