1. Let's start by defining the problem: We need to determine whether a given scalene triangle is obtuse or acute. 2. Recall the definitions: - An **acute triangle** has all angles less than 90 degrees. - An **obtuse triangle** has one angle greater than 90 degrees. 3. To classify the triangle, we can use the lengths of its sides and the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab\cos(C)$$ where $C$ is the angle opposite side $c$. 4. For a scalene triangle with sides $a$, $b$, and $c$, identify the longest side (say $c$). Then: - If $c^2 > a^2 + b^2$, the triangle is obtuse. - If $c^2 < a^2 + b^2$, the triangle is acute. - If $c^2 = a^2 + b^2$, the triangle is right-angled. 5. Since the user did not provide side lengths, the classification depends on comparing $c^2$ with $a^2 + b^2$. 6. Therefore, to determine if the scalene triangle is obtuse or acute, check the inequality: $$c^2 \gtrless a^2 + b^2$$ 7. If you provide the side lengths, I can compute and classify the triangle precisely.