What is x if (Csc^2(29.25/x)) / (Csc^2(10.75/x))=.3675?

This is for a calculus problem. It is about maximizing the angle of a field goal depending on distance. I would also like to know if this is insolvable. The distance between the goal posts is 18.5 ft and the distance between the goal post and the hash mark is 10.75 ft. The question is how far away from the goal post does the kicker need to be in order to optimize his angle. I think this equation would give me the correct distance, but if i'm wrong i'd like to know.