Given the information about the isosceles triangle, we have the following right triangle:
we can find half the distance from A to B by using the trigonometric function tangent as follows:
[tex]\begin{gathered} \tan (30)=\frac{\text{opposite side}}{adjacent\text{ side}}=\frac{6}{x} \\ \Rightarrow x=\frac{6}{\tan (30)}=\frac{6}{\frac{1}{\sqrt[]{3}}}=6\sqrt[]{3} \end{gathered}[/tex]
therefore, the distance from point A to point B is:
[tex]d(A,B)=2\cdot(6\sqrt[]{3})=12\sqrt[]{3}[/tex]
