We drew in the altitude AE in green to the right.  The green line is the
altitude of both triangles ABD and ADC.

Both triangles, ABD and ADC, have equal bases because AD is a median of triangle
ABC.  So BD = DC.  Let x = BD = DC, then BC = 2x

By the law of cosines,







x=0;  x-22cos(B)=0
         x = 22cos(B)

Ignore x=0, so x = 22cos(B)

Also by the law of cosines,






Divide through by 4



Substitute 22cos(B) for x








 

Angle B cannot be obtuse. It must be acute, so we ignore 
the negative sign



Using the SAS formula for the area of triangle ABC



We find sin(B) from 

We find BC = 2x = (2)( 22cos(B) ) = 44cos(B) =  =  




Edwin