In the diagram below, we have AD = 24 and ADB = 90 degrees. If sin A = 2/3 and sin C = 1/4, then what is DC?
+128474 sin A = 2/3
So tan A = 2 / [ 3^2 - 2^2 ] = 2 / sqrt 5
So
tan A = 2/sqrt 5
BD /AD = 2/sqrt 5
BD / 24 = 2/sqrt 5
BD = 48/sqrt 5
sin C =1/4
tan C = 1 / [ 4^2 - 1^2 ] = 1/ sqrt 15
So
tan C = 1/sqrt 15
BD / DC = 1/sqrt 15
(48 /sqrt 5) / DC = 1/sqrt 15
So
DC = (48/sqrt 5) / (1/sqrt 15)
DC = 48 (sqrt 15 / sqrt 5 )
DC = 48sqrt 3
