Problem 308 | Equilibrium of Concurrent Force System

$\Sigma F_H = 0$

$C \cos 45^\circ = T \cos 30^\circ$

$C = 1.2247T$
 

$\Sigma F_V = 0$

$T \sin 30^\circ + C \sin 45^\circ = 600$

$T \sin 30^\circ + (1.2247T) \sin 45^\circ = 600$

$1.366T = 600$

$T = 439.24 \, \text{ lb}$           answer
 

$C = 1.2247(439.24)$

$C = 537.94 \, \text{ lb}$           answer

$\Sigma F_y = 0$

$T \sin 75^\circ = 600 \sin 45^\circ$

$T = 439.23 \, \text{ lb}$           (okay!)
 

$\Sigma F_x = 0$

$C = T \cos 75^\circ + 600 \cos 45^\circ$

$C = 439.23 \cos 75^\circ + 600 \cos 45^\circ$

$C = 537.94 \, \text{ lb}$           (okay!)

 

 

$\dfrac{T}{\sin 45^\circ} = \dfrac{C}{\sin 60^\circ} = \dfrac{600}{\sin 75^\circ}$

$T = 439.23 \, \text{ lb}$           (okay!)

$C = 537.94 \, \text{ lb}$           (okay!)