Problem 312 | Equilibrium of Concurrent Force System

$\Sigma F_H = 0$

$F \cos 60^\circ + 200 \cos 45^\circ = 300 + P \cos 30^\circ$

$F = 317.16 + 1.7320P$
 

$\Sigma F_V = 0$

$F \sin 60^\circ = 200 \sin 45^\circ + P \sin 30^\circ$

$(317.16 + 1.7320P) \sin 60^\circ = 200 \sin 45^\circ + P \sin 30^\circ$

$274.67 + 1.5P = 141.42 + 0.5P$

$P = -133.25 \, \text{ N}$           answer
 

$F = 317.16 + 1.7320(-133.25)$

$F = 86.37 \, \text{ N}$           answer