🔺 Classifying Triangles Calculator
Classify triangles by sides and angles
How to Use This Calculator
Enter Three Side Lengths
Input the lengths of all three sides of the triangle (a, b, c).
Classify
Click "Classify Triangle" to analyze the triangle.
Review Classification
See how the triangle is classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
View Additional Info
See calculated angles, area, and perimeter of the triangle.
Classification Rules
Classification by Sides
- Equilateral: All three sides are equal (a = b = c)
- Isosceles: Exactly two sides are equal (a = b ≠c, or a = c ≠b, or b = c ≠a)
- Scalene: All three sides are different (a ≠b ≠c)
Classification by Angles
- Acute: All three angles are less than 90°
- Right: One angle is exactly 90°
- Obtuse: One angle is greater than 90°
Angle Calculation (Law of Cosines):
Angle A = arccos((b² + c² - a²) / (2bc))
Angle B = arccos((a² + c² - b²) / (2ac))
Angle C = arccos((a² + b² - c²) / (2ab))
Triangle Inequality Theorem
For a triangle to be valid:
- a + b > c
- a + c > b
- b + c > a
If any of these conditions fail, the sides cannot form a triangle.
About Classifying Triangles Calculator
The Classifying Triangles Calculator determines how a triangle should be classified based on its side lengths and angles. Triangles can be classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
When to Use This Calculator
- Geometry: Classify triangles in geometric problems
- Education: Learn triangle classification rules
- Construction: Identify triangle types for design purposes
- Engineering: Analyze triangular structures
- Trigonometry: Understand triangle properties for calculations
Why Use Our Calculator?
- ✅ Dual Classification: Classifies by both sides and angles
- ✅ Complete Analysis: Shows angles, area, and perimeter
- ✅ Validates Input: Checks triangle inequality theorem
- ✅ Educational: Helps understand triangle properties
- ✅ Free: No registration required
Triangle Classifications
By Sides:
- Equilateral: All sides equal
- Isosceles: Two sides equal
- Scalene: No sides equal
By Angles:
- Acute: All angles < 90°
- Right: One angle = 90°
- Obtuse: One angle > 90°
Examples
- Equilateral: 5, 5, 5 → All sides equal, all angles 60° (acute)
- Right Isosceles: 3, 3, 3√2 → Two sides equal, one right angle
- Scalene Acute: 5, 6, 7 → All sides different, all angles < 90°
- Scalene Obtuse: 2, 3, 4 → All sides different, one angle > 90°
Frequently Asked Questions
What are the different ways to classify triangles?
Triangles can be classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). A triangle has both classifications simultaneously.
Can a triangle be both equilateral and right?
No. An equilateral triangle has all angles equal to 60°, so it cannot have a 90° angle. An equilateral triangle is always acute.
Can a triangle be both isosceles and right?
Yes! A right isosceles triangle has two equal legs and one right angle. Its angles are 45°, 45°, and 90°.
How do you determine if a triangle is valid?
A triangle is valid if it satisfies the triangle inequality: the sum of any two sides must be greater than the third side (a + b > c, a + c > b, b + c > a).
What's the difference between isosceles and equilateral?
An isosceles triangle has exactly two equal sides. An equilateral triangle has all three sides equal. Note: An equilateral triangle is also isosceles, but typically we use "equilateral" when all sides are equal.
Can all three angles be acute?
Yes! An acute triangle has all three angles less than 90°. Examples include equilateral triangles (60°, 60°, 60°) and many scalene triangles.