F₁ = (F) one force

F₂ = (2F) second force

Let θ is angle between F₁ and F₂

Here angle made by resultant F_R is α with F₁

$$\begin{gathered} \therefore \mathrm{\alpha } = 90 \\ \tan \mathrm{\alpha } = \frac{{\mathrm{F}}_2 \sin \mathrm{\theta }}{{\mathrm{F}}_1 + {\mathrm{F}}_2 \cos \mathrm{\theta }} = \mathrm{\alpha } \\ \frac{{\mathrm{F}}_2 \sin \mathrm{\theta }}{{\mathrm{F}}_1 + {\mathrm{F}}_2 \cos \mathrm{\theta }} = \frac{1}{0} \\ {\mathrm{F}}_1 + {\mathrm{F}}_2 \cos \mathrm{\theta } = 0 \\ 2\mathrm{F} \cos \mathrm{\theta } = - \mathrm{F} \\ \cos \mathrm{\theta } = - \frac{1}{2} \\ \mathrm{\theta } = 120 \end{gathered}$$