a)
\begin{align} ΣF_x=0 =&\cssId{Step1}{F_{Ax} + F_{Bx} + F_{Cx}=0}\\[3px] &\cssId{Step2}{F_A + F_B * cos(α) + F_{Cx}=0}\\[3px] &\cssId{Step3}{F_{Cx}= -F_A -F_B * cos(α)}\\[3px] \end{align}
In the first step we make the summation of forces in the x-axis
In the second step we express F
Bx
as F
B
multiplying the cosine of the angle (doing trigonometry)
In the third step we isolate F
Cx
to one side of the equation and everything else to the other side so that you can solve the equation