In the diagram line segments AB and CD are of length 1 while angles ABC and CBD are 90∘ and 30∘ respectively. Find AC.[asy]
import geometry;
import graph;unitsize(1.5 cm);pair A, B, C, D;B = (0,0);
D = (3,0);
A = 2*dir(120);
C = extension(B,dir(30),A,D);draw(A--B--D--cycle);
draw(B--C);
draw(arc(B,0.5,0,30));label("A", A, NW);
label("B", B, SW);
label("C", C, NE);
label("D", D, SE);
label("30∘", (0.8,0.2));
label("90∘", (0.1,0.5));perpendicular(B,NE,C-B);
[/asy] geometrytrigonometrygeometry proposed