the question needs more clarification[which one of the two bases is longer],
so let ..in this trapezium [ call it ABCDE].....................
The given base[call BE] be the longer base and let the given side be AB (such that AB = CD)
therefore <BED = <CED and the required side is AD
Taking triangle CED {CE = (BE -AD)}
tan(<CED) = DC/CE
tan40 = 184/[775 - AD]
AD = 775 - 184/tan40......... = 555.72
Therefore the other side is 555.72mm