Acute Right or Obtuse Triangle Calculator

Triangle Classification Rule:

\[ \text{If } a² + b² > c² \text{ (acute)}, = c² \text{ (right)}, < c² \text{ (obtuse)} } \]

where c is the longest side

Triangle Type:

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1. What is Triangle Classification?

This calculator classifies triangles as acute, right, or obtuse based on the relationship between the squares of their sides. The classification helps in understanding the angle properties of the triangle.

2. How Does the Calculator Work?

The calculator uses the following rule:

\[ \text{If } a² + b² > c² \text{ (acute)}, = c² \text{ (right)}, < c² \text{ (obtuse)} } \]

Where:

\( a, b \) — The two shorter sides of the triangle
\( c \) — The longest side of the triangle

Explanation: The relationship between the squares of the sides directly corresponds to the type of angles in the triangle.

3. Importance of Triangle Classification

Details: Knowing whether a triangle is acute, right, or obtuse is fundamental in geometry and has applications in various fields including engineering, architecture, and computer graphics.

4. Using the Calculator

Tips: Enter the lengths of all three sides of the triangle. The calculator will automatically identify the longest side and perform the classification. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of input matter?
A: No, the calculator automatically sorts the sides to identify the longest side.

Q2: What if the sides don't form a valid triangle?
A: The triangle inequality theorem must be satisfied (sum of any two sides > third side). This calculator assumes valid triangle inputs.

Q3: Can this be used for any triangle?
A: Yes, this classification works for all triangles in Euclidean geometry.

Q4: How accurate are the results?
A: The classification is mathematically precise when correct side lengths are provided.

Q5: What about equilateral triangles?
A: All equilateral triangles are acute since all angles are 60°.