In the diagram below, we have AB = 24, angle ADB = 90, and angles A and C are acute. If sin A = 1/2 and sin C = 1/4, then what is BC?
sin A = BD/BA =1/2
BD / BA =1/2
BD =(1/2) BA
BD = (1/2)24 = 12
sin C = BD / BC = 1/4
BD/ BC =1/4
BC /BD = 4
BC = 12 (4) = 48
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BC = [24*sin(A)] / sin(C) ==> BC = (24 * 1/2) / 1/4 = 48
