1. What Are Triangle Inequalities?

Triangle inequalities are fundamental rules that determine whether three given lengths can form a triangle. The main principle states that the sum of any two sides must be greater than the third side.

2. How Does the Calculator Work?

The calculator checks three inequalities:

Where:

• \( a, b, c \) — Lengths of the three sides of the triangle

Explanation: For any triangle, the sum of any two sides must be greater than the remaining side. The calculator also identifies the largest side, which is opposite the largest angle in the triangle.

3. Importance of Triangle Inequalities

Details: These inequalities are essential in geometry for determining if three lengths can form a triangle, and in trigonometry for understanding angle-side relationships.

4. Using the Calculator

Tips: Enter three positive side lengths. The calculator will verify if they satisfy triangle inequalities and identify the largest side.

5. Frequently Asked Questions (FAQ)

Q1: What if two sides equal the third?
A: This forms a degenerate triangle (a straight line), which is not considered a valid triangle in most contexts.

Q2: Does this work for any triangle type?
A: Yes, these inequalities apply to all triangles - scalene, isosceles, and equilateral.

Q3: How does this relate to angles?
A: The largest angle is always opposite the longest side, and vice versa.

Q4: Can I use this for 3D triangles?
A: These inequalities apply to planar triangles. 3D cases require additional considerations.

Q5: What units should I use?
A: Any consistent length unit (cm, m, inches, etc.) as long as all sides use the same unit.