The smallest angle would be the angle opposite the smallest side. The angle is shown below:
To find the measure of the smallest angle, we would be using the cosine rule:
[tex]\cos \text{ C = }\frac{a^2+b^2-c^2}{2ab}[/tex]
Substituting the given sides, we have:
[tex]\begin{gathered} \cos \text{ C = }\frac{34^2+23^2-12^2}{2\times34\times23} \\ cos\text{ C = 0.98529} \\ C\text{ = }\cos ^{-1}0.98529 \\ C\text{ = }9.84^0 \end{gathered}[/tex]
