The forces acting on the mass are:
and 
are the components of the force from string tension, 
is gravity. The forces do not balance because the mass is undergoing circular
motion, with 
being the centripetal force. Note that the vertical
forces do balance, and there is no acceleration along the vertical axis...
will be the total tension force...
Note that these are only the magnitudes of the vectors... The magnitude of
is equal to the magnitude of 
.
Divide these equations, cancel common terms, and solve for
...
