Show Cos A = 1/12 in Square ABCD

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SUMMARY

To demonstrate that \( \cos a = \frac{1}{12} \) in square ABCD, the law of cosines is essential. The solution involves applying the law of cosines twice: first to triangle AEC to determine side EC, and then to triangle CED to calculate \( \cos a \). This method effectively utilizes the properties of supplementary angles and the geometric relationships within the square.

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View attachment 467In square ABCD need to show $cos a = \frac{1}{12}$
 

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

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