Triangle Calculator

- May 10, 2025
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This calculator helps you solve triangle problems by finding unknown sides, angles, area, perimeter, and more based on the information you provide.

Choose what you know about your triangle, input the values, and the calculator will determine all other properties.

Select what you know about your triangle

units
? The length of side a opposite to angle A.
units
? The length of side b opposite to angle B.
units
? The length of side c opposite to angle C.

Advanced Options

About Triangles

A triangle is a polygon with three sides and three angles. The sum of all internal angles in any triangle is always 180° (or π radians).

Triangle Types Based on Sides:
  • Equilateral Triangle: All three sides are equal in length, and all angles are equal (60° each).
  • Isosceles Triangle: Two sides are equal in length, and the angles opposite to these sides are equal.
  • Scalene Triangle: All three sides have different lengths, and all angles are different.
Triangle Types Based on Angles:
  • Acute Triangle: All three angles are less than 90°.
  • Right Triangle: One angle is exactly 90° (a right angle).
  • Obtuse Triangle: One angle is greater than 90°.
Triangle Solution Methods:
  • SSS (Side-Side-Side): When all three sides are known.
  • SAS (Side-Angle-Side): When two sides and the included angle are known.
  • ASA (Angle-Side-Angle): When two angles and the included side are known.
  • AAS (Angle-Angle-Side): When two angles and a non-included side are known.
  • SSA (Side-Side-Angle): When two sides and a non-included angle are known (the ambiguous case).
Key Triangle Formulas:

Area:

  • Area = (1/2) × base × height
  • Area = (1/2) × a × b × sin(C) (using two sides and the included angle)
  • Area = √(s(s-a)(s-b)(s-c)) (Heron's formula, where s is the semiperimeter)

Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

Law of Cosines:

c² = a² + b² - 2ab × cos(C)
cos(C) = (a² + b² - c²)/(2ab)
Additional Properties:
  • Perimeter: The sum of all three sides (a + b + c).
  • Semiperimeter (s): Half the perimeter, s = (a + b + c)/2.
  • Heights: The perpendicular distance from a vertex to the opposite side.
  • Medians: Lines from a vertex to the midpoint of the opposite side.
  • Incircle: The circle that is tangent to all three sides of the triangle.
  • Circumcircle: The circle that passes through all three vertices of the triangle.
  • Inradius (r): The radius of the incircle, r = Area/s.
  • Circumradius (R): The radius of the circumcircle, R = (abc)/(4×Area).

Understanding the Triangle Calculator

The Triangle Calculator is an excellent tool for anyone needing help with triangle problems. It provides users the ability to find unknown sides and angles, as well as the area and perimeter of triangles. All you have to do is enter the known values, and the calculator does the rest. This makes it easier for students and professionals alike to tackle Geometry problems without hassle.

How the Calculator Works

Using the Triangle Calculator is straightforward. You start by selecting what you already know about the triangle. The calculator supports several methods, including:

  • Three sides (SSS)
  • Two sides and an included angle (SAS)
  • Two angles and an included side (ASA)
  • Two angles and a non-included side (AAS)
  • Two sides and a non-included angle (SSA)
  • Right triangle calculations
  • Equilateral triangle properties

Each method has its own input fields that guide you in entering the necessary data.

Inputting Your Values

Once you’ve chosen your calculation method, the Triangle Calculator presents input fields specific to that method. For example, if you select the SSS method, you'll need to input the lengths of all three sides. If you choose SAS, you need to provide two sides and the included angle. This tailored approach makes it simple, ensuring you only enter the information that’s relevant to your calculation.

Getting Accurate Results

The Triangle Calculator is designed to deliver accurate results, regardless of the method you choose. After entering your values, the tool calculates various properties of the triangle, including:

  • Area
  • Perimeter
  • Type of triangle (e.g., scalene, isosceles, equilateral)
  • All three angles

This comprehensive output allows you to understand the triangle's characteristics thoroughly.

Visualising Your Triangle

One of the great features of the Triangle Calculator is the visualisation option. You can choose to see a diagram of your triangle based on the values entered. This visual aid helps you better understand the geometry at play and can be especially useful for learners who benefit from seeing concepts in action.

Advanced Options for Precision

The calculator also offers advanced options to help refine your results. You can adjust the number of decimal places in your results and choose your preferred angle unit—either degrees or radians. These settings allow for more precise calculations, which can be crucial in higher-level Mathematics or engineering contexts.

Understanding Triangle Theories

The Triangle Calculator isn't just about calculations; it also provides insights into triangle theory. Users can learn about different types of triangles based on sides and angles, as well as key formulas for area, perimeter, and more. This educational aspect makes the calculator a valuable resource for anyone looking to deepen their understanding of geometry.

Why Choose the Triangle Calculator?

In summary, the Triangle Calculator is a user-friendly tool that simplifies the process of solving triangle-related problems. By providing clear options for input, accurate calculations, and helpful visualisations, it supports both learning and practical application. Whether you’re a student, teacher, or a professional, this tool is a reliable companion for geometric challenges.