1. **Problem:** Classify the triangle with sides 6 in, 4 in, and 8 in by its angles and sides. 2. **Formula and rules:** - Use the Pythagorean theorem to check if the triangle is right-angled: $$a^2 + b^2 = c^2$$ where $c$ is the longest side. - Classify by sides: - Equilateral: all sides equal - Isosceles: two sides equal - Scalene: all sides different - Classify by angles: - Acute: all angles less than 90° - Right: one angle exactly 90° - Obtuse: one angle greater than 90° 3. **Intermediate work:** - Longest side is 8 in. - Check if right triangle: $$6^2 + 4^2 = 36 + 16 = 52$$ $$8^2 = 64$$ Since $$52 \neq 64$$, it is not a right triangle. 4. **Angle classification:** - Since $$6^2 + 4^2 < 8^2$$, the triangle is obtuse (one angle > 90°). 5. **Side classification:** - Sides are 6, 4, and 8, all different, so scalene. 6. **Answer:** The triangle is obtuse and scalene.