$(25$ Pts$)$ The system shown in the figure is in equilibrium. The weight of the box is $1000N.$ Determine the magnitude of the force $F1$ and the angel $P.$

$F_2=400(cos30(hat())+sin30(hat()))=346\mathrm{.}41$hat$()+200$hat$()$

$F_3=600(-\frac{4}{5}(hat())+\frac{3}{5}(tilde()))=-480$hat$()+360$hat$()$

$F_4=-1000$hat$(),|F_1|=\sqrt[\phantom{2}]{(-133\mathrm{.}59{)}^2+(-440{)}^2}=409\mathrm{.}83N$

$=ta{n}^{-1}(\frac{-440}{133\mathrm{.}59})=90-73\mathrm{.}11=16\mathrm{.}890$