Welcome to Math Help Forum!and , respectivelySince the angles are measured from the direction of , I assume they are all in the same sense (e.g. all anticlockwise). So we can write down the components along and perpendicular to , where is the ring, as follows:
Along :Perpendicular to :
We find the resultant force by summing these components:
Along ON:The magnitude of the resultant is therefore .
Perpendicular to ON: