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If you set the saw angle to $30^o$ and cut the board as in the diagram below then the angle at the heal of the cut measures $90^o + 30^o = 120^{o}$ and the angle at the toe, angle $CAB$ in the first diagram, measures $60^{o}.$ In the first diagram $E$ is the midpoint of $AB$ and the dark brown piece from $A$ to $B$ is a 2 by 4 on its side. Hence the distance from $D$ to $E$ is 3.5 inches. Suppose the distance from $C$ to $D$ is $x$ inches then the distance from $A$ to $E$ is \[\frac{x + 3.5}{\sqrt 3} \mbox{ inches.}\] If you want the interior dimension to be 12 inches then $x = 6$ inches and \[\frac{x + 3.5}{\sqrt 3} = \frac{9.5}{\sqrt 3} = 5.48 \mbox{ inches.}\] Thus the distance from $A$ to $B$ is $2 \times 5.48$ which is about 11 inches. Harley 



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