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