From FBD of pulley
$T = 200 \, \text{ lb}$
$\Sigma F_V = 0$
$B_V + T \sin 30^\circ = 200$
$B_V + 200 \sin 30^\circ = 200$
$B_V = 100 \, \text{ lb}$
$\Sigma F_H = 0$
$B_H = T \cos 30^\circ$
$B_H = 200 \cos 30^\circ$
$B_H = 173.20 \, \text{ lb}$
From FBD of beam
$\Sigma M_A = 0$
$8R_C = 4B_V$
$8R_C = 4(100)$
$R_C = 50 \, \text{ lb}$ answer
$\Sigma M_C = 0$
$8A_V = 4B_V$
$8A_V = 4(100)$
$A_V = 50 \, \text{ lb}$
$\Sigma F_H = 0$
$A_H = B_H$
$A_H = 173.20 \, \text{ lb}$
$R_A = \sqrt{{A_H}^2 + {A_V}^2}$
$R_A = \sqrt{173.20^2 + 50^2}$
$R_A = 180.27 \, \text{ lb}$
$\tan \theta_{Ax} = \dfrac{A_V}{A_H}$
$\tan \theta_{Ax} = \dfrac{50}{173.20}$
$\theta_{Ax} = 16.1^\circ$
Thus, $R_A = 180.27 \, \text{ lb}$ up to the right at $16.1^\circ$ from horizontal. answer