What is the length of the marked segment?



The marked segment is contained in the side of an equilateral triangle (of side length \(1\)).
It is the complement of the height of an equilateral triangle (of side length \(1\)).
Hence the length of the marked segment is \[ 1 - \dfrac{\sqrt{3}}{2} = \dfrac{2-\sqrt{3}}{2}\,.\]