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Triangle Calculator

Calculate triangle properties including area, perimeter, angles, and more using different input methods.

How to Use This Calculator

The Triangle Calculator offers two methods to calculate triangle properties:

  1. Three Sides (SSS):
    • Enter the length of all three sides
    • All sides must be positive numbers
    • The sum of any two sides must be greater than the third side
  2. Two Sides and Included Angle (SAS):
    • Enter the length of two sides
    • Enter the angle between these sides (in degrees)
    • The angle must be between 0° and 180°
  3. The calculator will show:
    • Area of the triangle
    • Perimeter
    • All three sides (if using SAS method)
    • All three angles
    • Height (perpendicular to side 1)

Understanding Triangle Calculations

The triangle calculator uses various geometric formulas to compute different properties of a triangle. It supports two methods of calculation:

  • Three Sides (SSS): Uses Heron's formula for area and the law of cosines for angles.
  • Two Sides and Included Angle (SAS): Uses trigonometric formulas including the law of sines and cosines.

When using the SSS method, the calculator first verifies if the sides can form a valid triangle using the Triangle Inequality Theorem. This theorem states that the sum of any two sides must be greater than the third side.

For the SAS method, the calculator uses these formulas:

  • Area = (1/2) × a × b × sin(C), where C is the included angle
  • Third side = √(a² + b² - 2ab×cos(C))
  • Other angles are found using the law of sines

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