The resultant of two forces, one double of the other magnitude, is perpendicular to the smaller of two forces. The angle between the two force is

See figure. P and Q (2P) are two forces and their resultant is R. The angle between P and Q is $\mathrm{\alpha }$.

From figure, $\cos \mathrm{\theta }=\frac{\mathrm{P}}{\mathrm{Q}}=\frac{\mathrm{P}}{2\mathrm{P}}=\frac{1}{2}$
$\begin{array}{l}\therefore \mathrm{\theta }={\cos }^{-1}\left(\frac{1}{2}\right)={60}^{\circ }\\ \mathrm{So},\mathrm{\alpha }={180}^{\circ }-{60}^{\circ }={120}^{\circ }\end{array}$