Trigonometry Triangle question

[Bushy]

In square ABCD need to show $cos a = \frac{1}{12}$

 

[MarkFL]

While I haven't worked this problem yet, I am thinking the law of cosines may help, along with the relationship between supplementary angles.

 

[Fantini]

I gave it some thought, and I believe applying law of cosines twice will do the trick. First you apply to the triangle $AEC$ to find side $EC$, and then apply it to the triangle $CED$ to find $\cos a$.