Identical balls suspended on threads of equal length fixed at one point were charged with the same charges

Identical balls suspended on threads of equal length fixed at one point were charged with the same charges of the same name. The balls pushed off, and the angle between the threads became 60 degrees. After immersing the ball in a liquid dielectric, the angle between the filaments decreased to 50 degrees. Find the dielectric constant of the medium. Disregard the buoyancy.

Let us write down the equations of the projection of the forces acting on the ball on the axis Y:
m * g = T * sin (α / 2)
on the X-axis:
Fq = T * cos (α / 2) where the tensile force of the thread, Fq is the Coulomb force. Let us divide these equations:
Fq / m * g = ctg (α / 2)
Then the ratio of the Coulomb forces in the first and second cases will be:
Fq1 / Fq2 = ctg (α / 2) / ctg (ß / 2) where α and ß are angles in the first and second cases, so the Coulomb force is inversely proportional to έ we get:
έ2 / έ1 = ctg (ß / 2) / ctg (α / 2) = ctg (25) / √3 = 2.14 / 1.73 = 1.27