In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?
sin A = 1/3
sin A = BD / AB
BD / AB = 1/3
BD / 24 = 1/3
BD = (1/3)(24) = 8
sin C = 1/2
arcsin (1/2) = 30° = C
BD = 8
So since triangle CBD = 30 -60 - 90
Then BC = 2 BD = 2 * 8 = 16
+1752 
