Question

The three sided lengths are 7,8,9 classify the triangle as an acute obtuse or right triangle

Answer 1

Using the law of cosines to find m∠B:

`\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ 2ac\cdot\cos (B)=a^2+c^2-b^2 \\ \cos (B)=(a^2+c^2-b^2)/(2ac) \\ \cos (B)=(8^2+7^2-9^2)/(2\cdot8\cdot7) \\ \cos (B)=(32)/(112) \\ B=\arccos ((32)/(112)) \\ B=73.4\text{ \degree} \end{gathered}`

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