To classify the triangle by its angles and sides, let’s analyze the given information step by step.

Step 1: Classification by Angles

The triangle has angles measuring $30^\circ$, $40^\circ$, and $110^\circ$.

1. Obtuse Triangle: One of the angles ($110^\circ$) is greater than $90^\circ$, which makes this an obtuse triangle.

2. Not Acute: An acute triangle has all angles less than $90^\circ$, which this triangle does not satisfy.

3. Not Right: There is no angle equal to $90^\circ$, so this is not a right triangle.

Step 2: Classification by Sides

The triangle does not provide information about the side lengths directly, but based on the given angles:

1. Scalene Triangle: All three angles are different, so all three sides must also be different. This means the triangle is scalene.

2. Not Isosceles or Equilateral: Isosceles triangles have at least two equal angles, and equilateral triangles have three equal angles. Neither condition is satisfied here.

Final Classification

• Scalene
• Obtuse

Would you like more details or have additional questions? Here are some questions to expand your understanding:

1. How can you calculate side lengths using trigonometric ratios for such a triangle?
2. What is the relationship between the angles and side lengths in a scalene triangle?
3. What are the specific properties of an obtuse triangle?
4. How can the triangle inequality theorem be used to validate the sides of this triangle?
5. How do we determine if a triangle is acute, right, or obtuse using just the angles?

Tip: Remember that classifying triangles involves both angles and sides—focus on identifying unique properties!