makes this one easier. I found the pure algebra solution very hard to follow (although the trig solution could probably be converted into an easier algebraic solution than the one I have seen.)
Work in feet, so this is an unit square. Call the unknown dimension x and the smaller of the two acute angles Θ
The right edge length can be expressed as
The top and bottom edge can be expressed as
x + sin(Θ) + x cos(Θ)
Setting both of those expressions equal to 1 and solving for x gives you
x = (1- cos(Θ))/ sin(Θ)
x = (1-sin(Θ))/ (1+cos(Θ))
Setting these two expressions of x equal to each other, cross multiplying, and using the fact that 1-cos²=sin² eventually yields the fact that sin(Θ)=½, confirming Larry's observation that the angles are 30 and 60.
Using this value for sin(Θ) in either formula for x yields x=2-√3, and multiplying by 12 to get back to inches gives ~3.215.
Maybe less math for the next puzzle!!!