Using the law of cosines to find m∠B:
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ 2ac\cdot\cos (B)=a^2+c^2-b^2 \\ \cos (B)=\frac{a^2+c^2-b^2}{2ac} \\ \cos (B)=\frac{8^2+7^2-9^2}{2\cdot8\cdot7} \\ \cos (B)=\frac{32}{112} \\ B=\arccos (\frac{32}{112}) \\ B=73.4\text{ \degree} \end{gathered}[/tex]
Since B is the largest angle (because it's opposite to the longer side), then angles A and C are smaller. In consequence, the three angles are smaller than 90°, which means that the triangle is acute
