Triangle Calculator

Solve Triangle Sides, Angles, and Area with Step-by-Step Logic

Select what you know about the triangle, then enter the values to calculate the rest.

Calculation Examples

Calculation Case Result
Sides: 3, 4, 5 (Right Triangle) Area = 6
Equilateral triangle side 6 Area = 15.588
Hypotenuse (legs 5 and 12) 13

How to Solve a Triangle?

To solve a triangle, enter at least three values (SSS, SAS, or ASA). The tool utilizes the Pythagorean theorem $a^2 + b^2 = c^2$ for right triangles and the Laws of Sines and Cosines for oblique cases. It also handles the ambiguous SSA case where two solutions may exist.

How this Calc Works?

The triangle calc computes sides, angles, area, perimeter, heights or median based upon the input you give. For SSS (side-side-side), it uses the Law of Cosines to find the angles you want with precision. For AAS (angle-angle-side), it will use the Law of Sines which should also give you the exact measurements.

SSA (side-side-angle) situations may give you one or two answers, called the ambiguous case. This is an ideal resource for geometry students, architects, or engineers needing a timely, guaranteed triangle completion for design or analysis.

Right Angled Triangle Diagram

Useful Tips 💡

  • Ensure your angles are in degrees (totaling 180°).
  • For SSA cases, check if the input provides two possible solutions.

📋Steps to Calculate

  1. Enter known sides or angles.

  2. Select triangle type if needed.

  3. Click "Calculate" to find area and missing values.

Mistakes to Avoid ⚠️

  1. Entering side lengths that cannot form a triangle (e.g., sides 1, 2, and 10).
  2. Mixing up the "Side-Side-Angle" case, which can result in two different valid triangles.
  3. Forgetting that the sum of interior angles must always equal exactly 180 degrees.

Practical Applications📊

  1. Calculate area for geometry homework or design projects.

  2. Pair with our Area Converter for unit adjustments.

  3. Explore different triangle types for educational practice.

Questions and Answers

What is meant by a triangle calculator?

In its most general sense, a three-sided polygon solver is a calculator that calculates the area, side lengths and angles of any triangle based on a singular measurement. For example, if one was using the CalcMate angle calculator, one would input the values of the trigon's three side lengths. It will use any number of formulas, for example Heron's formula for area or trigonometric relationships for those angles. It will give you accurately right, scalene or isosceles triangles.

How to determine the area of a triangle?

If the base ($b$) and height ($h$) are known, the area is $A = \frac{1}{2}bh$. For three known sides, the calculator uses Heron’s Formula: $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter: $s = \frac{a+b+c}{2}$.

How to use a right triangle calculator?

To find some other trilateral values, take a look at right triangle angle calculator. A right triangle calc is a device that uses the Pythagorean theorem (a² + b² = c²) to get at the hypotenuse or missing side and trigonometry to get the angles, giving you a swift and accurate output.

How do you find the angle of a triangle?

To get the angle of a triangle, just input the known sides or angles into the required fields and click on the 'Calculate' button. It covers systems that can be solved with the law of sines or cosines on the missing angles ensuring that all angles total equal 180 degrees.

How do I determine a triangle's exterior measurement?

You can input two of the triangles sides, an angle, and other properties in the triangle side calculator. It solves the three-sided polygon's side based on its category by using the ratio of two sides by the angle, or other laws of trigons to find missing part with the appropriate accuracy.

What formulas ensure the accuracy of this tool?

We use the Law of Sines, Law of Cosines, and Heron’s Formula, all of which are standard principles approved by the Mathematical Association of America (MAA).

Can the Triangle Calculator support 3D geometry problems?

The Triangle solver is designed for 2D trigons, solving for sides, angles, or area. For 3D geometry (e.g., tetrahedrons), use 2D results as a foundation for further calculations or employ specialized software for volumetric analysis.

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Disclaimer: This calculator is designed to provide helpful estimates for informational purposes. While we strive for accuracy, financial (or medical) results can vary based on local laws and individual circumstances. We recommend consulting with a professional advisor for critical decisions.