we know that
AB=CD
AD=BC
in the right triangle DBC
[tex]cos\ 30=\frac{adjacent\ side\ angle\ 30}{hypotenuse}[/tex]
[tex]adjacent\ side\ angle\ 30=DC\\ hypotenuse=BD=2\ in[/tex]
substitute
[tex]cos\ 30=\frac{DC}{2}[/tex]
[tex]DC=2*cos\ 30\\\\DC=2*\frac{\sqrt{3} }{2} \\\\ DC=\sqrt{3}\ in[/tex]
[tex]DC=\sqrt{3}\ in=1.73\ in[/tex]
remember that
AB=CD
so
[tex]AB=\sqrt{3}\ in=1.73\ in[/tex]
therefore
the answer is
the length of line segment AB is [tex]\sqrt{3}\ in[/tex]
