Solve any triangle with sides and angles using Law of Sines, Law of Cosines, and trigonometric principles. Calculate area, perimeter, heights, and all triangle properties with professional geometric solutions.
SSS: Three sides → Law of Cosines
SAS: Two sides + included angle → Law of Cosines
ASA/AAS: Two angles + any side → Law of Sines
SSA: Two sides + non-included angle → Ambiguous case analysis
a/sinA = b/sinB = c/sinC = 2R. Used when you know two angles and one side (AAS/ASA) or two sides and a non-included angle (SSA ambiguous case). Fundamental for triangle solving and trigonometric applications.
a² = b² + c² - 2bc·cosA. Used when you know three sides (SSS) or two sides and the included angle (SAS). Essential for finding unknown sides and angles in non-right triangles with comprehensive geometric accuracy.
A + B + C = 180° (or π radians). The fundamental property that the sum of interior angles in any triangle always equals 180 degrees. Used to find missing angles when two angles are known in triangle solving.
Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2. Used to calculate triangle area when all three side lengths are known. Provides accurate area calculation without needing height measurements or angle information.
This triangle calculator provides comprehensive geometric calculations using established mathematical formulas including Law of Sines, Law of Cosines, and trigonometric principles. Results are intended for educational, academic, engineering, and professional reference purposes. For critical architectural, engineering, or construction applications requiring exact geometric validation, always verify calculations with professional CAD software and established engineering standards. While we strive for mathematical accuracy using proper geometric algorithms, this tool should complement comprehensive geometric analysis in professional and academic contexts.
This advanced triangle calculator implements comprehensive geometric analysis based on established principles of plane geometry, trigonometry, and triangle solving methodologies. Each calculation follows precise geometric definitions and analytical methods that form the foundation of professional mathematics, engineering, and architectural education across diverse disciplines.
Mathematical Foundation: Triangle geometry and trigonometric principles
The calculator applies fundamental geometric principles using precise mathematical formulas that follow established geometric standards. The implementation handles comprehensive triangle solving including Law of Sines, Law of Cosines, angle sum theorem, and Heron's formula with proper geometric methods. The calculator performs detailed geometric analysis, provides comprehensive triangle summaries, and offers step-by-step explanations of triangle solutions according to professional mathematical and engineering standards.
Angle Relationships: Sine, cosine, and tangent functions in triangles
Beyond basic calculation, the calculator provides comprehensive trigonometric analysis including angle relationships, side ratios, and trigonometric function applications in geometric contexts. The implementation follows trigonometric principles for triangle solving, handles different angle units and conversion factors, and provides intuitive understanding of geometric relationships. This includes automatic unit conversion, proper trigonometric function application, and clear communication of geometric properties according to mathematical standards.
Triangle Properties: Classification and characteristic analysis
The calculator provides comprehensive geometric interpretation including triangle type classification, property analysis, and practical implications of geometric measures. The implementation follows geometric principles for spatial interpretation, handles different triangle types and dimensional relationships, and provides contextual analysis for various application domains. This includes proper assessment of triangle properties in relation to geometric constraints, analysis of dimensional relationships in practical contexts, and interpretation of geometric results according to analytical best practices.
Practical Implementation: Triangles across professional domains
Beyond theoretical calculation, the calculator provides comprehensive real-world application analysis showing how triangle geometry solves practical problems across various domains. It includes scenario-based examples from architecture and construction (structural analysis), engineering and design (force vectors), navigation and surveying (triangulation), computer graphics (3D modeling), and scientific research (spatial relationships). This contextual understanding enhances the practical value of geometric concepts beyond mathematical calculation, connecting triangle principles to tangible problem-solving across professional, technical, scientific, and educational contexts.
This advanced triangle calculator supports all triangle types: scalene, isosceles, equilateral, acute, obtuse, and right triangles. It uses Law of Sines, Law of Cosines, and trigonometric principles to solve any triangle given sufficient information (SSS, SAS, ASA, AAS, SSA configurations) with professional geometric accuracy and comprehensive solution steps. Additional features include triangle type classification, area calculation, perimeter computation, height determination, and comprehensive geometric analysis that supports both basic triangle solving and advanced geometric applications across educational, engineering, and professional contexts where reliable geometric computation enhances spatial understanding and practical decision-making.
You need exactly 3 known values with at least one side length. Valid combinations include: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and any side), or SSA (two sides and non-included angle). The calculator automatically detects the configuration and applies the appropriate geometric solution method. Each solving method follows geometric principles with proper formula application, dimensional consistency checking, and comprehensive result interpretation that enhances spatial reasoning and practical application of geometric concepts in academic and professional contexts requiring triangle computation.
The calculator uses fundamental geometric principles including Law of Sines (a/sinA = b/sinB = c/sinC), Law of Cosines (a² = b² + c² - 2bc·cosA), triangle angle sum theorem (A+B+C=180°), Heron's formula for area, and trigonometric functions. Each calculation follows established mathematical standards with comprehensive step-by-step explanations. The calculator automatically handles unit relationships and provides results in appropriate units, ensuring dimensional accuracy and practical applicability across measurement systems used in academic, engineering, and professional geometric applications requiring precise triangle solutions.
Yes, the calculator supports both degrees and radians. Simply select your preferred angle unit from the dropdown menu. The calculator automatically handles unit conversions and maintains mathematical consistency throughout all calculations, ensuring accurate results regardless of your chosen angle measurement system. The calculator provides comprehensive unit-aware calculations with proper trigonometric function application, ensuring reliable geometric solutions for both degree-based and radian-based mathematical applications in academic and professional contexts.
The calculator computes all triangle properties: all three side lengths, all three angles, area, perimeter, semi-perimeter, heights from each vertex, medians, angle bisectors, circumradius, inradius, triangle type classification, and comprehensive geometric analysis with professional mathematical precision. Additional calculations include trigonometric ratios, area using different formulas, and geometric relationships that provide complete triangle characterization for educational purposes, engineering applications, architectural design, and mathematical analysis requiring comprehensive geometric understanding.
Calculations use precise geometric formulas with JavaScript's floating-point arithmetic. Results are accurate to 6 decimal places for professional applications. The calculator follows mathematical standards and handles ambiguous SSA cases with proper geometric analysis, providing reliable solutions for educational, engineering, and mathematical applications. Additional accuracy features include proper rounding methods, significant figure handling, and error margin consideration that ensure reliable results for educational purposes, preliminary engineering calculations, and professional geometric analysis where mathematical precision supports informed decision-making in triangle-based applications.