007 Components of a force parallel and perpendicular to the incline

$\theta = \alpha + \beta$

$\theta = \arctan (3/4) + \arctan (5/12)$

$\theta = 59.49^\circ$
 

$F_x = 500 \cos \theta = 500 \cos 59.49^\circ$

$F_x = 253.85 \, \text{ kN}$           answer
 

$F_y = -500 \sin \theta = -500 \sin 59.49^\circ$

$F_y = -430.77 \, \text{ kN}$           answer