Question 1110789
Here is a sketch of what the mirror and its diagonals would look like
(with lengths in inches).
{{{drawing(300,650,-6,6,-13,13,
green(triangle(-5,0,5,0,0,12)),
green(triangle(-5,0,0,-12,0,12)),
green(rectangle(-0.3,-0.3,0.3,0.3)),
line(-5,0,0,12),line(0,12,5,0),
line(5,0,0,-12),line(0,-12,-5,0),
locate(-2.7,0,green(5)),locate(2.3,0,green(5)),
locate(0.1,6.5,green(12)),locate(0.1,-5.5,green(12)),
locate(-2.5,6,side),
red(arc(5,0,4,4,180,247.38)),
locate(3.5,1,red(A)),
red(arc(0,12,4,4,67.38,90)),
locate(0.2,10.7,red(B))
)}}} As per Pythagorean theorem, {{{side=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13}}} .
The first part of the answer to the math problem is that
the length of wood frame material you need is
{{{4*13inches=highlight(52inches)}}} .
 
If you can buy exactly {{{52inches}}}{{{"="}}}{{{4&1/3}}}{{{ft}}}{{{"="}}}{{{"4 ft 4 inches"}}} ,
it would cost {{{(52inches)*(1ft/"12inches")*("$1.14"/"1 ft")="$4.94"}}} .
However, if you cannot buy that exact length
because the framing material is sold by the foot,
in whole-number lengths only,
you would need to buy {{{5ft}}} of framing, 
and that would cost {{{5ft*("$1.14"/"1 ft")="$5.70"}}} .
 
{{{tan(red(A))=12/5=2.4}}} --> {{{red(A)=67.38^o}}} .
{{{red(B)=90^o-red(A)=90^o-67.38^o=22.62^o}}} .
Those are the angles you would use for cutting the ends of the framing pieces.
The angles at the corners of the glass part of the mirror,
and at the corners of the finished framed mirror are
{{{2*red(A)=2*67.38^o=highlight(134.76^o)}}} , and
{{{2*red(b)=2*22.62^o=highlight(45.24^o)}}} .