So I had this mechanics problem
and it was pretty straight forward until I reached two final equations, if any of them can be solved, the problem is solved.
One of the equations is a fourth degree equation in terms of the normal contact force on the disc, and it can’t even be treated as a quadratic, so pretty hopeless.
The other one, which, as I later saw, was used in the model answer to get the angle theta was $ 880\sin{\theta} = 400\tan{\theta} +20(9.81) $. Now I had tried to play with sines, cosines, tangents, trig identities but for the life of me I cannot think of a way after all that except maybe using a taylor polynomial of second or third degree or using a recursive formula to approximate the roots, but because what was written in the model answer was this equation followed by “solving for theta we get $27.1$ degrees and $50.2$ degrees” I feel that this equation has an exact solution which is beyond me. Could anybody please clarify the way to solve such an equation?
Thanks in advance.