As its an integer, the easiest seems to be just to iterate (try) different values for n to get the result or as youve done plot in desmos. Its an increasing function so just keep going. Nothing exact comes to mind and the hints are fairly poor.
Doing the previous suggestion
1 - pi^2 x / 8 + .. = sqrt(0.95)
gives 1/x = 48.7 and you could include the second quadratic term as well and solve as it may be significant or just try (it works in this case) based on a linear series expansion with may be trying a value either side. A similar thing would be to use pythagoras so cos^2n = (1-sin^2)^n and use a (linear) series approximation for sin/binomial, though if either was the way, Id have expected a hint.