In $\triangle A C D$ , You Are Given $$\angle C = 90 ^ { \circ } , \angle A = 60 ^ { \circ }$$

Multiple Choice

In $\triangle A C D$ , you are given $$\angle C = 90 ^ { \circ } , \angle A = 60 ^ { \circ }$$ and $A C = 9$ . If $B$ is a point on $\overline { C D }$ and $\angle B A C = 45 ^ { \circ }$ , find $B D$ .

A) $B D = 6$
B) $B D =$ $3 ( 3 - \sqrt { 3 } )$
C) $B D =$ $6 \sqrt { 3 }$
D) $B D = 3$
E) $B D =$ $9 ( \sqrt { 3 } - 1 )$