Since 2010 · Powering 2M+ tool runs every month
Since 2010
Add to Chrome

My Toolbox

Automatic Mode

No saved tools yet.

Go Premium
Related tools
Next step
Heron's Formula Calculator
More tools
Right Triangle CalculatorPythagorean Theorem CalculatorHypotenuse CalculatorAngle Bisector CalculatorLaw of Cosines CalculatorLaw of Sines Calculator
Home Page > Math > Geometry Calculators

General Triangle Solver

MiniWebtool’s General Triangle Solver calculates missing sides and angles from suitable SSS, SAS, ASA, AAS, or SSA information. Worked trigonometric steps accompany the resulting area and perimeter, with the available measurements determining which triangle solutions are possible.

Need help using this tool? Ask AI
Gemini (copy & open)

For Gemini, paste the copied question into the chat. You can also copy it below.

View the question

Free to useNo sign-up requiredInstant Results
General Triangle SolverTry it now — free ▼
Law of cosines for the missing side, then the angles add to 180°

Enter any three known sides or angles below to get the missing sides, angles, area and perimeter, with the steps.

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.

At a Glance

General Triangle Solver finds the missing sides, angles, area and perimeter of a triangle from three known values in SSS, SAS, ASA, AAS or SSA form. It shows a labeled diagram and step-by-step working.

General Triangle Solver: features at a glance
FeatureWhat you getGood for
Five configurationsSolves SSS, SAS, ASA, AAS and SSA. Enter any three known values for sides a, b, c and angles A, B, C, and leave the rest empty.Geometry and trigonometry problems with mixed givens
Laws and formulasUses the Law of Cosines, the Law of Sines and Heron's formula, with the steps shown for your values.Learning which law applies to which case
SSA ambiguous caseDetects when two sides and a non-included angle give 0, 1 or 2 valid triangles and returns the valid solution.Avoiding a missed second triangle
Complete resultsReturns all three sides and all three angles, plus the area and perimeter.Surveying, roofing and structural layout checks
ValidationChecks the triangle inequality and that the angles sum to 180 degrees, and detects the triangle type.Catching impossible inputs
Labeled diagramA diagram of the triangle labels the vertices, sides and angles.Visualizing the solved triangle

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.

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. Use consistent units: Enter all side lengths in the same unit (for example, all in meters or all in inches). The calculator does not have a unit selector, so the results are returned in that same unit: area is in square units and perimeter is in the same unit as the sides. Angles must always be entered in degrees.
  3. Enter the known values: Input your three known values in the corresponding fields. Leave the unknown fields empty.
  4. Click Calculate: The solver automatically detects your triangle type and applies appropriate formulas.
  5. 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.

Units Used in Results

The sides can be entered as plain numbers with no unit attached. The results simply keep whatever unit you used, so mixing units (such as one side in feet and another in meters) will give incorrect answers. Angles are always in degrees, with each angle between 0 and 180.

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

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

Chat with your favorite AI

Gemini (copy & open)

For Gemini, paste the copied question into the chat. You can also copy it below.

View the question

Geometry Calculators:

Math SolverWhat would you like to solve?

Math Solver

Try
Browse expression examples

Choose an example to fill the input, edit its numbers, then Solve. log uses base 10; use ln for the natural logarithm.

Numbers & factors

Fractions & division

Powers, roots & logs

Algebra & equations

Calculus

Geometry & trigonometry

Top & Updated:

Triangle Orthocenter CalculatorTriangle Centroid CalculatorArea of Equilateral Triangle CalculatorView all →
Home Page > Math > Geometry Calculators > General Triangle Solver