Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Geometry Calculators > General Triangle Solver

General Triangle Solver

The ultimate tool to solve any triangle. Input three known values (e.g., SSS, SAS, ASA, AAS) and automatically calculate all missing sides, angles, area, and perimeter using the law of sines, law of cosines, and Heron's formula.

General Triangle Solver
Try Example Triangles:
SSS 3-4-5 Right SAS a=5, b=7, C=60° AAS a=10, A=30°, B=70° SSA b=8, c=6, A=40°
Sides
Angles (degrees)
Enter exactly 3 known values. At least one must be a side length.

Embed General Triangle Solver Widget

About General Triangle Solver

Welcome to the General Triangle Solver, a comprehensive tool for solving any triangle using advanced trigonometric methods. Whether you know three sides (SSS), two sides and an angle (SAS or SSA), or two angles and a side (AAS/ASA), this calculator determines all missing elements including sides, angles, area, and perimeter with step-by-step explanations.

What is a General Triangle Solver?

A General Triangle Solver is a mathematical tool that calculates all unknown elements of a triangle (sides, angles, area, perimeter) when given any three valid pieces of information. It uses the Law of Sines, Law of Cosines, and Heron's formula to solve triangles in any configuration: SSS, SAS, ASA, AAS, or SSA.

Key Features

Triangle Solution Methods

The Law of Cosines

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:

Law of Cosines
$$c^2 = a^2 + b^2 - 2ab\cos(C)$$

This law is essential for solving SSS (three sides) and SAS (two sides and included angle) triangles.

The Law of Sines

The Law of Sines states that the ratio of a side to the sine of its opposite angle is constant:

Law of Sines
$$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$

This is useful for ASA, AAS, and SSA configurations.

Heron's Formula for Area

Heron's formula calculates the area of a triangle when all three sides are known:

Heron's Formula
$$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$

where $s = \frac{a+b+c}{2}$ is the semi-perimeter.

How to Use This Calculator

  1. Identify known values: Determine which three values you know: sides (a, b, c) and/or angles (A, B, C). The angle A is opposite side a, B is opposite side b, and C is opposite side c.
  2. Enter the known values: Input your three known values in the corresponding fields. Leave the unknown fields empty.
  3. Click Calculate: The solver automatically detects your triangle type and applies appropriate formulas.
  4. Review the results: Examine the complete solution including all sides and angles, area, perimeter, an interactive diagram, and step-by-step calculation explanations.

Triangle Configurations Explained

What is the SSA Ambiguous Case?

The SSA (Side-Side-Angle) ambiguous case occurs when you know two sides and an angle opposite one of them. This configuration may result in zero, one, or two valid triangles, depending on the relative sizes of the known values. The calculator determines which case applies and provides the valid solution.

Important Triangle Properties

Applications

Frequently Asked Questions

What is a General Triangle Solver?

A General Triangle Solver is a mathematical tool that calculates all unknown elements of a triangle (sides, angles, area, perimeter) when given any three valid pieces of information. It uses the Law of Sines, Law of Cosines, and Heron's formula to solve triangles in any configuration: SSS, SAS, ASA, AAS, or SSA.

What is the Law of Cosines?

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The formula is c² = a² + b² - 2ab·cos(C), where a, b, c are sides and C is the angle opposite to side c. It's used to solve triangles when you know SSS (three sides) or SAS (two sides and included angle).

What is the Law of Sines?

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). It's useful for solving ASA, AAS, and SSA triangle configurations.

What is the SSA ambiguous case?

The SSA (Side-Side-Angle) ambiguous case occurs when you know two sides and an angle opposite one of them. This configuration may result in zero, one, or two valid triangles, depending on the relative sizes of the known values. The calculator determines which case applies and provides the valid solution.

How is triangle area calculated using Heron's formula?

Heron's formula calculates the area of a triangle when all three sides are known: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter: s = (a+b+c)/2. This formula works for any triangle regardless of its shape.

Additional Resources

Reference this content, page, or tool as:

"General Triangle Solver" at https://MiniWebtool.com/general-triangle-solver/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 23, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

Angle Bisector CalculatorNew
Circle Calculator
Circumscribed Circle (Circumcircle) CalculatorNew
Heron's Formula CalculatorNew
Inscribed Circle (Incircle) CalculatorNew
Law of Cosines Calculator
Law of Sines Calculator
Pythagorean Theorem Calculator
Regular Polygon CalculatorNew
Right Triangle Calculator

Geometry Calculators:

Top & Updated:

Random Name PickerRandom PickerRelative Standard Deviation CalculatorBatting Average CalculatorFPS ConverterLine CounterERA CalculatorMAC Address GeneratorSort NumbersInstagram User ID LookupRemove SpacesMAC Address LookupFeet and Inches to Cm ConverterWord to Phone Number ConverterFacebook User ID LookupRandom Truth or Dare GeneratorSum CalculatorRandom Quote GeneratorSHA256 Hash GeneratorPercent Off CalculatorBitwise CalculatorNumber of Digits CalculatorYouTube Thumbnail DownloaderSquare Root (√) CalculatorLog Base 10 CalculatorOn Base Percentage CalculatorSun, Moon & Rising Sign Calculator 🌞🌙✨Saturn Return CalculatorSlugging Percentage CalculatorOPS CalculatorSalary Conversion CalculatorRandom IMEI GeneratorVertical Jump CalculatorRoman Numerals ConverterPhone Number ExtractorSlope and Grade CalculatorMP3 LooperScientific Notation to Decimal ConverterCompound Growth CalculatorCm to Feet and Inches ConverterDecimal to BCD ConverterRandom Poker Hand GeneratorAudio SplitterWHIP CalculatorVideo to Image ExtractorBinary to Gray Code ConverterMerge VideosRandom Birthday GeneratorRandom Superpower GeneratorNumber to Word ConverterAI ParaphraserOutlier CalculatorRemove AccentFirst n Digits of PiRandom Activity GeneratorTime Duration CalculatorBCD to Decimal ConverterText FormatterOctal CalculatorNumber ExtractorQuotient and Remainder CalculatorRandom Movie PickerWord Ladder GeneratorDay of Year CalendarRandom Fake Address GeneratorGray Code to Binary ConverterInvisible Text GeneratorLove Compatibility CalculatorCompare Two StringsAI Punctuation AdderFile Size ConverterExponential Integral CalculatorGamma Function CalculatorWAR CalculatorWhat is my Lucky Number?Binary to BCD ConverterPercent Growth Rate CalculatorSHA512 Hash GeneratorCM to Inches ConverterIP Address to Hex ConverterImage SplitterMaster Number CalculatorAdd or Replace Audio in VideoRandom Sound Frequency GeneratorPER CalculatorDay of the Year Calculator - What Day of the Year Is It Today?Video CropperConnect the Dots GeneratorRandom Group GeneratorReverse VideoVideo CompressorBCD to Hex ConverterNatural Log CalculatorStair CalculatorHeight Percentile CalculatorYouTube Channel StatisticsAdd Text to ImageStandard Error CalculatorAdd Prefix and Suffix to TextEmail ExtractorURL ExtractorList of Prime NumbersSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorMedian CalculatorLeap Years ListList RandomizerBreak Line by CharactersAverage CalculatorModulo CalculatorPVIFA CalculatorHypotenuse CalculatorRemove Audio from VideoActual Cash Value CalculatorAngel Number CalculatorLog Base 2 CalculatorRoot Mean Square CalculatorSum of Positive Integers CalculatorSHA3-256 Hash GeneratorAI Sentence Expander📅 Date CalculatorLbs to Kg ConverterHex to Decimal ConverterConvolution CalculatorMAC Address AnalyzerRandom String GeneratorRemove Leading Trailing SpacesAmortization CalculatorMarkup CalculatorPVIF CalculatorName Number CalculatorDecimal to Hex ConverterDaily Time Savings CalculatorLorem Ipsum GeneratorReadability Score CalculatorKeyword Density CheckerBionic Reading ConverterText to Speech ReaderFancy Text GeneratorZalgo Text GeneratorUpside Down Text GeneratorASCII Art GeneratorList Difference CalculatorText Column ExtractorText to SQL List ConverterInvisible Character RemoverStock Average CalculatorPosition Size CalculatorMargin Call CalculatorShort Selling Profit CalculatorFutoshiki GeneratorHashi (Bridges) Puzzle GeneratorSlitherlink Puzzle GeneratorWord Search Puzzle GeneratorCrossword Puzzle MakerCryptogram GeneratorWord Scramble GeneratorBingo Card GeneratorTip CalculatorCurrency Converter401(k) CalculatorRoth IRA CalculatorRetirement CalculatorSocial Security Benefits CalculatorPension CalculatorRMD CalculatorSIP CalculatorMutual Fund CalculatorStock Profit Loss CalculatorDividend Reinvestment CalculatorDollar Cost Averaging CalculatorBusiness Loan CalculatorPersonal Loan CalculatorDebt Payoff CalculatorDebt Consolidation CalculatorNet Worth CalculatorBudget CalculatorSavings Goal CalculatorEmergency Fund CalculatorAPI TesterASCII Table ReferenceWebhook TesterSchema Markup GeneratorRobots.txt GeneratorXML Sitemap GeneratorOpen Graph CheckerDomain Age CheckerWHOIS LookupDNS LookupHeadline AnalyzerPage Speed CheckerRedirect CheckerHreflang Tag GeneratorDomain Trust CheckerBroken Link CheckerAI Content DetectorAI Text HumanizerAI Blog Title GeneratorAI Email WriterAI Hashtag GeneratorAI Slogan GeneratorAI Article Outline GeneratorAI Token CounterInstagram Engagement Rate CalculatorTikTok Engagement Rate CalculatorYouTube Earnings EstimatorYouTube Tag ExtractorYouTube Comment PickerInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorTwitter/X Character CounterTwitter/X Timestamp ConverterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorSocial Media Post Time OptimizerSocial Media Username CheckerCTR CalculatorROAS CalculatorInfluencer ROI CalculatorForce CalculatorAcceleration CalculatorVelocity CalculatorMomentum CalculatorProjectile Motion CalculatorKinetic Energy CalculatorPotential Energy CalculatorWork and Power CalculatorDensity CalculatorPressure CalculatorIdeal Gas Law CalculatorFree Fall CalculatorTorque CalculatorHorsepower CalculatorDilution CalculatorChemical Equation BalancerStoichiometry CalculatorPercent Yield CalculatorEmpirical Formula CalculatorBoiling Point CalculatorTitration CalculatorMole/Gram/Particle ConverterLED Resistor CalculatorVoltage Divider CalculatorParallel Resistor CalculatorCapacitor Calculator555 Timer CalculatorWire Gauge CalculatorTransformer CalculatorRC Time Constant CalculatorPower Factor CalculatorDecibel (dB) CalculatorImpedance CalculatorResonant Frequency CalculatorGrade CalculatorFinal Grade CalculatorWeighted Grade CalculatorTest Score CalculatorSignificant Figures CalculatorStudy Timer (Pomodoro)Long Division CalculatorRounding CalculatorCompleting the Square CalculatorRatio Calculatorp-Value CalculatorNormal Distribution CalculatorPercentile CalculatorFive Number Summary CalculatorCross Multiplication CalculatorLumber CalculatorRebar CalculatorPaver CalculatorInsulation CalculatorHVAC Sizing CalculatorRetaining Wall CalculatorCarpet CalculatorSquare Footage Calculator⏱️ Countdown Timer⏱️ Online Stopwatch⏱️ Hours Calculator🕐 Military Time Converter📅 Date Difference Calculator⏰ Time Card Calculator⏰ Online Alarm Clock🌐 Time Zone Converter🌬️ Wind Chill Calculator🌡️ Heat Index Calculator💧 Dew Point CalculatorFuel Cost CalculatorTire Size Calculator👙 Bra Size Calculator🌍 Carbon Footprint Calculator⬛ Aspect Ratio CalculatorOnline Notepad🖱️ Click Counter🔊 Tone Generator📊 Bar Graph Maker🥧 Pie Chart Maker📈 Line Graph Maker📷 OCR / Image to Text🔍 Plagiarism Checker🚚 Moving Cost Estimator❄️ Snow Day Calculator🎮 Game Sensitivity Converter⚔️ DPS Calculator🎰 Gacha Pity Calculator🎲 Loot Drop Probability Calculator🎮 In-Game Currency ConverterMultiplication Table GeneratorLong Multiplication CalculatorLong Addition and Subtraction CalculatorOrder of Operations Calculator (PEMDAS)Place Value Chart GeneratorNumber Pattern FinderEven or Odd Number CheckerAbsolute Value CalculatorCeiling and Floor Function CalculatorUnit Rate CalculatorSkip Counting GeneratorNumber to Fraction ConverterEstimation CalculatorCubic Equation SolverQuartic Equation SolverLogarithmic Equation SolverExponential Equation SolverTrigonometric Equation SolverLiteral Equation SolverRational Equation SolverSystem of Nonlinear Equations SolverPoint-Slope Form CalculatorStandard Form to Slope-Intercept ConverterEquation of a Line CalculatorParallel and Perpendicular Line CalculatorDescartes' Rule of Signs CalculatorRational Root Theorem CalculatorSigma Notation Calculator (Summation)Product Notation Calculator (Pi Notation)Pascal's Triangle GeneratorBinomial Theorem Expansion CalculatorParabola CalculatorHyperbola CalculatorConic Section IdentifierRegular Polygon CalculatorIrregular Polygon Area CalculatorFrustum CalculatorTorus Calculator3D Distance CalculatorGreat Circle Distance CalculatorCircumscribed Circle (Circumcircle) CalculatorInscribed Circle (Incircle) CalculatorAngle Bisector CalculatorTangent Line to Circle CalculatorHeron's Formula CalculatorCoordinate Geometry Distance CalculatorVolume of Revolution CalculatorSurface of Revolution CalculatorParametric Curve GrapherRiemann Sum CalculatorTrapezoidal Rule CalculatorSimpson's Rule CalculatorImproper Integral CalculatorL'Hôpital's Rule CalculatorMaclaurin Series CalculatorPower Series CalculatorSeries Convergence Test CalculatorInfinite Series Sum CalculatorAverage Rate of Change CalculatorInstantaneous Rate of Change CalculatorRelated Rates SolverOptimization Calculator (Calculus)Gradient Calculator (Multivariable)Divergence CalculatorCurl CalculatorLine Integral CalculatorSurface Integral CalculatorJacobian Matrix CalculatorNewton's Method CalculatorRREF Calculator (Row Echelon Form)Matrix Inverse CalculatorMatrix Multiplication CalculatorDot Product CalculatorCross Product CalculatorVector Magnitude CalculatorUnit Vector CalculatorAngle Between Vectors CalculatorNull Space CalculatorColumn Space CalculatorCramer's Rule CalculatorMatrix Diagonalization CalculatorQR Decomposition CalculatorCholesky Decomposition Calculator