Use cosine law to find b:
[tex]b^2=a^2+b^2-2ac*cosB[/tex][tex]\begin{gathered} b^2=(20cm)^2+(20cm)^2-2(20cm)(20cm)*cos120º \\ b^2=400cm^2+400cm^2-800cm^2*(-0.5) \\ b^2=400cm^2+400cm^2+400cm^2 \\ b^2=1200cm^2 \\ b=\sqrt{1200cm^2} \\ b=20\sqrt{3}cm \\ b\approx34.64cm \end{gathered}[/tex]
Then, the distance between A and C is 20√3 cm or approximately 34.64 cm
