Which expression can be used to determine the length of segment ZY?

Answer:
Option 2:   [tex]YZ = \sqrt{(3)^{2}+(8)^{2} }[/tex]
Step-by-step explanation:We can see that XYZ is forming right angled triangle in the given figure where XY is Perpendicular.XZ is Base.YZ is Hypotenuse . Length of XY is 3 units (refer figure)Length of XZ is 8 units (refer figure)Now to calculate length of ZY we will use Pythagoras theorem i.e.
[tex](Hypotenuse)^{2} = (Perpendicular)^{2} +(Base)^{2}[/tex]
By applying this theorem :
[tex](YZ)^{2} = (XY)^{2} +(XZ)^{2}[/tex]
[tex](YZ)^{2} = (3)^{2} +(8)^{2}[/tex]
⇒[tex]YZ = \sqrt{(3)^{2}+(8)^{2} }[/tex]
Thus Option 2 is the correct expression to determine length of ZY i.e.[tex]YZ = \sqrt{(3)^{2}+(8)^{2} }[/tex]