Triangle Solver

Results

Enter values above to solve the triangle

Understanding Triangle Solutions

Triangle Solution Methods

SSS (Side-Side-Side)

Uses three sides to solve the triangle using the law of cosines

SAS (Side-Angle-Side)

Uses two sides and their included angle

ASA (Angle-Side-Angle)

Uses two angles and the included side

AAS (Angle-Angle-Side)

Uses two angles and a non-included side

Key Formulas

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines

c² = a² + b² - 2ab·cos(C)

Area

Area = ½·a·b·sin(C)

Triangle Properties

  • Sum of angles = 180°
  • Longest side is opposite to largest angle
  • Triangle inequality: sum of any two sides > third side
  • Area = ½·base·height
  • Perimeter = sum of all sides

Special Cases

Right Triangle

  • One angle = 90°
  • Pythagorean theorem applies
  • a² + b² = c²

Equilateral Triangle

  • All sides equal
  • All angles = 60°
  • Area = (√3/4)·a²

Isosceles Triangle

  • Two sides equal
  • Two angles equal
  • Height bisects base

Applications of Triangle Solutions

Surveying

Used in land surveying and distance calculations

Engineering

Essential in structural design and force analysis

Navigation

Used in GPS systems and maritime navigation