Consider the triangle ABX.
Determine the length of AX by using the pythagoras theorem.
[tex]\begin{gathered} (AX)^2=(BX)^2-(AB)^2 \\ =(30)^2-(24)^2 \\ AX=\sqrt[]{324} \\ =18 \end{gathered}[/tex]The length of XY is twice of side AX. So XY = 36
Consider trinagle XYZ.
Detertmine the length of side YZ by using pythagoras theorem.
[tex]\begin{gathered} (YZ)^2=(60)^2-(36)^2 \\ YZ=\sqrt[]{2304} \\ =48 \end{gathered}[/tex]The length of side YC is half of YZ so YC = 24.
Determine the length of side AC by using pyhtagras theorem in triangle AYC.
[tex]\begin{gathered} AC=\sqrt[]{(AY)^2+(YC)^2} \\ =\sqrt[]{(18)^2+(24)^2} \\ =\sqrt[]{900} \\ =30 \end{gathered}[/tex]So length of AC is 30.
Answer: 30
