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A 2.0 kg ball tied to a string fixed to the ceiling is pulled to one side by a force F. Just before the ball is released, (a) how large is the force F that is holding the ball in position and (b) what is the tension in the string?

Also given: the angle between the string and the ceiling is 30 degrees.

I understand everything up to the point that I've found the components of T and calculated:

sum of x forces = Tcos30 (since in eqb sum of x forces=0)

sum of y forces = Tsin30 (since in eqb sum of y forces =0)

In the solutions manual, they are then taking F/w (force vector in positive-x direction/ weight vector in negative-y direction) = Tcos30/Tsin30

I don't understand why they are dividing F by w. I see that this will eliminate T so that you can solve for F, however, the decision to divide F by w seems arbitrary. Either that or I'm fundamentally missing something. Any insight?