We can use the law of cosines to find the angle across the 34.2-length side:
[tex]\begin{gathered} (34.2)^2=(20.2)^2+(21.3)^2-2(20.2)(21.3)\cos C \\ \Rightarrow1169.64=408.04+453.64-860.52\cos C \\ \Rightarrow\cos C=\frac{1169.64-408.04-453.64}{-860.52}=-0.358 \\ \Rightarrow C=\cos ^{-1}(-0.358)=111 \\ C=111\degree \end{gathered}[/tex]
therefore, the measure of the largest angle is 111 degrees
