Trigonometry! #28

Geometry Level 4

For a $\Delta ABC$ ,

$c=3cm$

$b=6cm$

$\cos(\angle BAC)=\frac {1}{8}$

Find the length of $AD$ , the angle bisector of $\angle BAC$ , such that $D$ lies on $\overline{BC}$ .

This problem is part of the set Trigonometry.