In rectangle ABCD, shown here, CE is perpendicular to BD . If BC = sqrt(3) and DC = 2, what is CE?
BD = sart [ BC^2 + BD^2 ] =sqrt [ (sqrt 3)^2 + 2^2 ] = sqrt [ 3 + 4 ] = sqrt [7]
sin BDC = BC / BD = sqrt (3) / sqrt (7)
Using the Law of Sines
EC / sin BDC = DC /sin 90
EC / (sqrt (3) / sqrt (7)) = 2 /1
EC = 2sqrt (3) / sqrt (7) = 2sqrt (21) / 7
