In order to verify if the triangle is acute, right or obtuse, let's compare the square of the greater side and the sum of squares of the smaller sides:
[tex]\begin{gathered} \text{greater side:} \\ 12^2=144 \\ \text{smaller sides:} \\ 10^2+3^2=100+9=109 \end{gathered}[/tex]
Since the square of the greater side is greater than the sum of squares of the smaller sides (that is: a² > b² + c²), the triangle is obtuse
