Triangle Calculator

Triangle Calculator

Understanding Triangles: A Comprehensive Guide

What is a Triangle Calculator?

A triangle calculator is a specialized tool that helps solve various triangle-related problems. Our calculator handles multiple calculation methods including SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), and right triangle calculations, making it useful for geometry, trigonometry, and real-world applications.

Key Features of Our Triangle Calculator

  • Multiple calculation methods: SSS, SAS, ASA, and right triangle
  • Comprehensive results: All sides, angles, area, perimeter, heights
  • Triangle types: Identifies if triangle is scalene, isosceles, or equilateral
  • Right triangle features: Special calculations for right triangles
  • Visual representation: Shows triangle shape based on inputs

Triangle Formulas Used

Law of Cosines

c² = a² + b² – 2ab cos(C)

Used to find a side when two sides and the included angle are known (SAS)

Law of Sines

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

Used to find sides/angles when two angles and a side are known (ASA)

Pythagorean Theorem

a² + b² = c²

Used for right triangles to find any missing side

Types of Triangles

Triangles can be classified by their sides and angles:

By Sides

  • Equilateral: All sides equal, all angles 60°
  • Isosceles: Two sides equal, two angles equal
  • Scalene: All sides and angles different

By Angles

  • Acute: All angles < 90°
  • Right: One angle = 90°
  • Obtuse: One angle > 90°

Practical Applications of Triangle Calculations

Triangle geometry is used in many real-world situations:

  • Construction: Roof framing, bridge design
  • Navigation: Triangulation for GPS and mapping
  • Art and design: Creating perspective and composition
  • Physics: Force vector calculations
  • Astronomy: Measuring distances to stars

Common Triangle Measurements

Measurement Formula
Perimeter P = a + b + c
Area (base-height) A = ½ × base × height
Area (Heron’s formula) A = √[s(s-a)(s-b)(s-c)] where s = ½P
Height (from side a) hₐ = 2A/a