In the given circuit , V_C = 50 V and $R=50 \mathrm{\Omega }.$ The values of C and V_R are

${\mathrm{V}}_{\mathrm{C}}^2+{\mathrm{V}}_{\mathrm{R}}^2={\mathrm{V}}^2$

${50}^2+{\mathrm{V}}_{\mathrm{R}}^2={\mathrm{V}}^2$

${\mathrm{V}}_{\mathrm{R}}^2={110}^2-{50}^2$

${\mathrm{V}}_{\mathrm{R}}=\sqrt{{110}^2-{50}^2}$

${\mathrm{V}}_{\mathrm{R}}=\sqrt{160\times 60}\simeq 98\mathrm{V}$

Then, ${\mathrm{I}}_R=\frac{98}{50}$ A                $(\therefore \mathrm{R}=50\mathrm{\Omega })$

Also,   $\mathrm{I}={\mathrm{I}}_{\mathrm{R}}=\frac{110}{\sqrt{{\mathrm{R}}^2+{\mathrm{X}}_{\mathrm{C}}^2}}\Rightarrow \frac{98}{50}=\frac{110}{\sqrt{{50}^2+{\mathrm{X}}_{\mathrm{C}}^2}}$

Find X_C and then use ${\mathrm{X}}_{\mathrm{c}}=\frac{1}{\mathrm{\omega C}}$ to find C.

$C=104\mu F$