Suggest the length of the shorter side is x. The \(\displaystyle{120}^{\circ}\) angle is opposite to the longer side. So the angle opposite to the shorter side is \(\displaystyle{180}-{120}={60}^{\circ}\). Now we have a triangle with one side being x, and the two others: 17cm and 28cm, because the diagonals of a parallelogram bisect each other. Use the Law of Cosines to solve this.

\(\displaystyle{x}^{{2}}={28}^{{2}}+{17}^{{2}}-{2}{\left({28}\right)}{\left({17}\right)}{{\cos{{60}}}^{\circ}}\)

\(\displaystyle{x}^{{2}}={597}\)

\(\displaystyle{x}=\sqrt{{597}}\)

\(\displaystyle{x}\approx{24.4}\) cm

The shorter side is approximately 24.4cm long.

\(\displaystyle{x}^{{2}}={28}^{{2}}+{17}^{{2}}-{2}{\left({28}\right)}{\left({17}\right)}{{\cos{{60}}}^{\circ}}\)

\(\displaystyle{x}^{{2}}={597}\)

\(\displaystyle{x}=\sqrt{{597}}\)

\(\displaystyle{x}\approx{24.4}\) cm

The shorter side is approximately 24.4cm long.