Problem 318 | Equilibrium of Concurrent Force System

$F_{AB} \cos 30^\circ = 20 \sin 45^\circ$

$F_{AB} = 16.33 \, \text{ kN}$
 

$\Sigma F_x = 0$

$F_{BC} = 20 \cos 45^\circ + F_{AB} \sin 30^\circ$

$F_{BC} = 20 \cos 45^\circ + 16.33 \sin 30^\circ$

$F_{BC} = 22.31 \, \text{ kN}$

$F_{CD} \cos 15^\circ = P \sin 60^\circ$

$F_{CD} = 0.8966P$
 

$\Sigma F_x = 0$

$P \cos 60^\circ + F_{CD} \sin 15^\circ = F_{BC}$

$P \cos 60^\circ + (0.8966P) \sin 15^\circ = 22.31$

$0.7320P = 22.31$

$P = 30.48 \, \text{ kN}$  ←   answer