Analyze some Data

I have an Equilateral triangle (the length of each side is 1) and inside this triangle additional side is α (the distance between the base of Equilateral triangle and α is ε ) . I want to find the length of (α) by proving this formula | α | ≥ ½ + √(¼ -√3 ε +ε²), where ε is (epsilon( ε ) <0.13)