Solution:

The answer is $(\mathbf{E})$. Let $A, B, C$ be the three friends and $T$ the treasure. By symmetry $C T$ is perpendicular to $A B$.

Consider the triangle $A C T$. $\widehat{A C T}=30^\circ$ and $C T=2 A T$; this is enough to conclude that $A C T$ is hemi-equilateral (that is, it is half of an equilateral triangle). In particular $\widehat{C A T}=90^\circ$ and by the Pythagorean theorem $A C=\sqrt{C T^2-A T^2}=\sqrt{2^2-1^2}=\sqrt{3}$.