What is the length of the marked segment?



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