In rectangle ABCD, shown here, CE is perpendicular to BD . If BC = sqrt(3) and DC = 2, what is CE?
Angle EDC = arctan (sqrt(3)/2) = 40.9 degrees
then angle ECD = 180 - 90 - 40.9 = 49.1 degrees
cos (ECD) = adj / hyp
cos (49.1) = EC / 2
EC = 1.3 units
BD = √7
[ABCD] = 2√3
CE = [ABCD] / √7