What is the length of the marked segment?




The triangle \(ABC\) is a right triangle and \(AB\) is the hypotenuse.
Since the triangle legs have lengths \(1\) and \(\dfrac{1}{2}\) respectively, by Pythagoras's theorem the hypotenuse has length \[\sqrt{1^2 + \Big(\dfrac{1}{2}\Big)^2}=\sqrt{\dfrac{5}{4}}=\dfrac{\sqrt{5}}{2}\,.\]