Triangle Calculator

What is Triangle Calculator?

A triangle calculator helps you find all properties of triangles using various input methods. Whether you know sides, angles, or combinations of both, this calculator can determine the remaining measurements using fundamental geometric principles like the Law of Sines, Law of Cosines, and triangle inequality theorem.

Input Methods

• SSS (Side-Side-Side): Given all three sides, calculate all angles using the Law of Cosines
• SAS (Side-Angle-Side): Given two sides and the included angle, find the third side and remaining angles
• ASA (Angle-Side-Angle): Given two angles and the included side, calculate the remaining sides and angle
• AAS (Angle-Angle-Side): Given two angles and any side, determine all remaining measurements
• SSA (Side-Side-Angle): Given two sides and a non-included angle - may have ambiguous solutions

Triangle Properties

• Area: Calculated using Heron's formula: √(s(s-a)(s-b)(s-c)) where s is the semi-perimeter
• Perimeter: Sum of all three sides (a + b + c)
• Altitudes: Perpendicular distances from each vertex to the opposite side
• Medians: Lines from each vertex to the midpoint of the opposite side
• Semi-perimeter: Half the perimeter, used in many triangle formulas

Triangle Classifications

• By Angles:
• Acute: All angles less than 90°
• Right: One angle exactly 90°
• Obtuse: One angle greater than 90°
• By Sides:
• Scalene: All sides different lengths
• Isosceles: Two sides equal length
• Equilateral: All sides equal length (also all angles = 60°)

Ambiguous Case (SSA)

• When given two sides and a non-included angle, multiple triangles may be possible
• This occurs when the given angle is acute and opposite the shorter of the two given sides
• The calculator will show both solutions when they exist
• Always verify which solution fits your specific problem context

Important Formulas

• Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
• Law of Cosines: c² = a² + b² - 2ab·cos(C)
• Triangle Inequality: Sum of any two sides must be greater than the third side
• Angle Sum: All angles in a triangle sum to exactly 180°
• Area Formula: Area = ½ × base × height = ½ab·sin(C)

FAQ - Triangle Calculator