In the diagram below, we have AB = 24 and angle ADB = 90. If sin A = 3/4 and sin C = 1/4, then what is DC?
sin A = 3/4 = BD / BA
3/4 = BD / 24
(3/4)(24) = BD = 18
sin C = 1/4 = BD / BC
4BD = BC
4 (18) = BC = 72
DC = sqrt [ 72^2 - 18^2 ] = sqrt [ 18^2 ( 4^2 - 1^2) ] = 18 sqrt (15)
