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}
1. In the first step we make the summation of forces in the x-axis
2. In the second step we express FBx as FB multiplying the cosine of the angle (doing trigonometry)
3. In the third step we isolate FCx to one side of the equation and everything else to the other side so that you can solve the equation