This type of problem is also readily solved in another manner. Look again at the two equilibrium equations, $\sum _{}^{} {\mathrm{F}}_{\mathrm{x}}=0$ and $\sum _{}^{} {\mathrm{F}}_{\mathrm{y}}=0$:

$$\begin{gathered} \sum _{}^{} {\mathrm{F}}_{\mathrm{x}}={\mathrm{F}}_1 \cos (49.3^{\circ })+{\mathrm{F}}_2 \cos (24.9^{\circ })=0 \\ \sum _{}^{} {\mathrm{F}}_{\mathrm{y}}={\mathrm{F}}_1 \sin (49.3^{\circ })+{\mathrm{F}}_2 \sin (24.9^{\circ })-\mathrm{P}=0 \end{gathered}$$