AIME 2006a Problem 7

An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region $C$ to the area of shaded region $B$ is 11/5. Find the ratio of shaded region $D$ to the area of shaded region $A.$ [asy] defaultpen(linewidth(0.7)+fontsize(10)); for(int i=0; i<4; i=i+1) { fill((2i,0)--(2i+1,0)--(2i+1,6)--(2i,6)--cycle, mediumgray); } pair A=(1/3,4), B=A+7.5dir(-17), C=A+7dir(10); draw(B--A--C); fill((7.3,0)--(7.8,0)--(7.8,6)--(7.3,6)--cycle, white); clip(B--A--C--cycle); for(int i=0; i<9; i=i+1) { draw((i,1)--(i,6)); } label("$\mathcal{A}$", A+0.2dir(-17), S); label("$\mathcal{B}$", A+2.3dir(-17), S); label("$\mathcal{C}$", A+4.4dir(-17), S); label("$\mathcal{D}$", A+6.5dir(-17), S);[/asy]