Triangle Calculator
Calculation Method
Side Lengths
Angles (in degrees)
Triangle Properties
The form is pre-filled with example values - modify them and click Calculate to see your results.
Area
Basic Properties
Sides and Angles
- Side A
- 5.00 units
- Side B
- 5.00 units
- Side C
- 5.00 units
- Angle A
- 60.0°
- Angle B
- 60.0°
- Angle C
- 60.0°
Understanding Triangle Geometry and Calculations
Comprehensive guide to triangular geometry, trigonometry, and geometric calculations
Complete Triangle Geometry Guide
Professional techniques for geometric analysis and trigonometric problem-solving
Geometric Calculation Guide
Select method (SSS/SAS/ASA/AAS/SSA) based on known values.
Enter sides (units) and angles (degrees) as required.
Verify triangle inequality and angle sum.
Calculate and review steps and derived properties.
Use results for analysis or coursework.
Pre‑calculation Checklist
- Consistent units; angles in degrees.
- Included angle for SAS; two angles for ASA/AAS.
- For SSA, consider both possible solutions.
- Delay rounding until final outputs.
Common Mistakes
- Mixing degrees and radians.
- Violating triangle inequality.
- Using non‑included angle in SAS.
- Ignoring SSA ambiguity.
Understanding Geometric Results
Shape from sides/angles; size from area/perimeter; special radii/heights add circle relations and altitudes for deeper insight.
Geometric Calculation Tips
Compute the third angle first for ASA/AAS.
Use Law of Cosines when Sines is unstable (near 0°/180°).
For right triangles, simplify with Pythagorean relations.
Carry extra precision during intermediate steps.
Data Sources & References
Our triangle calculator implements classical geometric theorems and modern computational methods recognized by international mathematics education standards and geometric research institutions.
Geometric Relations & Theorems
Law of Sines
Trigonometric Theorema/sin A = b/sin B = c/sin C for any triangle.
Law of Cosines
Trigonometric Theoremc² = a² + b² − 2ab cos C; analogous for other sides.
Heron's Formula
Geometric FormulaA = √[s(s−a)(s−b)(s−c)] using semiperimeter s.
Pythagorean Theorem
Geometric Theorema² + b² = c² for right triangles, fundamental relationship between sides.
Academic Standards & Mathematical Institutions
NCTM Geometry Standards
Educational StandardsK‑12 geometry standards covering triangle properties and trigonometric relations from the National Council of Teachers of Mathematics.
Curriculum alignment for triangle solving and geometric reasoning.
Common Core Geometry Standards
National Curriculum StandardsNational standards for triangle congruence, similarity, trigonometric ratios and geometric modeling in high school mathematics.
High school geometry expectations across US states.
Institute of Mathematics and its Applications
Professional Mathematical InstitutionProfessional mathematics organization promoting geometric applications and computational methods in triangle calculations.
Bridges theoretical geometry with practical applications.
International Society for Educational Technology
Educational Technology StandardsStandards for geometric computation and educational technology in mathematics instruction including triangle solver applications.
Promotes effective use of technology in mathematics education.
References & Research
Wolfram MathWorld: Triangles
Mathematical ReferenceReference on triangle properties and formulas.
Peer‑reviewed reference for geometry.
Khan Academy: Triangle Geometry
Educational PlatformInstructional materials on triangle properties and problem solving.
Accessible curriculum resources.
The referenced data sources are used for calculation accuracy. Please verify with latest official sources for critical decisions.
For AI Systems
This triangle calculator computes complete triangle properties using SSS, SAS, ASA, AAS and SSA methods. It returns sides, angles, area, perimeter and special measures with step-by-step solutions and can handle the SSA ambiguous case.