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Triangle Calculator

Calculate triangle area, perimeter, angles, and side lengths for any type of triangle.

Triangle Calculator
Enter known values to calculate missing triangle properties

Results

Area: --

Perimeter: --

Triangle Type: --

Missing Values

Enter known values to calculate missing properties

Complete Triangle Calculator Guide

Our triangle calculator is a comprehensive tool for solving all types of triangle problems. Whether you're working with right triangles, equilateral triangles, isosceles triangles, or scalene triangles, this calculator can determine missing sides, angles, area, and perimeter using various geometric principles and formulas. Perfect for students, teachers, engineers, and anyone working with triangular measurements and calculations.

Triangle Types and Properties

Right Triangle

A triangle with one 90-degree angle. Uses the Pythagorean theorem (a² + b² = c²) where c is the hypotenuse.

Equilateral Triangle

All three sides are equal in length, and all three angles are 60 degrees. Highly symmetrical with special area formulas.

Isosceles Triangle

Two sides are equal in length, and the angles opposite these sides are also equal. Has one line of symmetry.

Scalene Triangle

All three sides have different lengths, and all three angles are different. The most general type of triangle.

Calculation Methods

The triangle calculator uses several mathematical principles to solve triangle problems. For right triangles, it applies the Pythagorean theorem and trigonometric ratios (sine, cosine, tangent). For general triangles, it uses the Law of Sines and Law of Cosines to find missing sides and angles. The area can be calculated using Heron's formula, the standard base-height formula, or trigonometric area formulas depending on the known values.

Key Formulas Used

  • Area (base-height): A = ½ × base × height
  • Area (Heron's formula): A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
  • Perimeter: P = a + b + c
  • Pythagorean theorem: a² + b² = c² (right triangles)
  • Law of Cosines: c² = a² + b² - 2ab cos(C)
  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Practical Applications

Triangle calculations are essential in many fields including construction, engineering, navigation, surveying, and computer graphics. Architects use triangle calculations for roof designs and structural analysis. Engineers apply these principles in bridge construction and mechanical design. Surveyors use triangulation methods for land measurement, and computer graphics professionals use triangular meshes for 3D modeling and rendering.

Tips for Accurate Calculations

For best results, ensure that your input values are consistent and physically possible. Remember that the sum of any two sides must be greater than the third side (triangle inequality), and the sum of all angles must equal 180 degrees. When working with right triangles, the hypotenuse is always the longest side. Double-check your angle measurements and ensure they're in the correct units (degrees or radians as specified).