Make a straight line perpendicular to AB from point C, and the vertical foot is E ... Because AB=8, DC=3, ABCD is an isosceles trapezoid, so

BE=(8-3)/2=2.5, because angle A = 60 and angle B = 60, according to BC=2*BE is in the right triangle BCE. So BC=5

(In a right triangle, the opposite side of 30 is half of the hypotenuse)