Problem $1$:

The cargo box as shown weighs $W=1200lb.$ The force $P=800lb$ is just sufficient to lift the box off the

floor. The $2-$D concurrent force system of the joint O is shown as well. Using the equilibrium equations:

${\displaystyle \underset{i=1}{\overset{n}{}}}{F}_{ix}=0$;${\displaystyle \underset{i=1}{\overset{n}{}}}{F}_{iy}=0,$

Determine the tension force in the cable $T$;

Determine the corresponding value of $.$