The equilibrium equations for beam $\mathrm{BC}$ are:

$$\begin{gathered} \sum _{}{\mathrm{M}}_{\mathrm{C}}=-(75 \mathrm{kN})(2.5 \mathrm{m}) \\ -(5.0 \mathrm{m}) {\mathrm{F}}_1 \sin (35.0^{\circ })=0 \\ \sum _{}{\mathrm{F}}_{\mathrm{x}}={\mathrm{C}}_{\mathrm{x}}- {\mathrm{F}}_1 \cos (35.0^{\circ })=0 \\ \sum _{}{\mathrm{F}}_{\mathrm{y}}={\mathrm{C}}_{\mathrm{y}}-75 \mathrm{kN}-{\mathrm{F}}_1 \sin (35.0^{\circ })=0 \end{gathered}$$