Triangle Calculator

Calculate triangle properties (sides, angles, area, perimeter) using SSS, SAS, ASA, AAS, or SSA with step-by-step solutions.

Calculator

Select a calculation mode and enter the required values to calculate triangle properties.

Complete User Guide

Calculation Modes

  • SSS (Side-Side-Side): Three sides given. Uses Law of Cosines and Heron's formula.
  • SAS (Side-Angle-Side): Two sides and included angle. Uses Law of Cosines.
  • ASA (Angle-Side-Angle): Two angles and included side. Uses Law of Sines.
  • AAS (Angle-Angle-Side): Two angles and non-included side. Uses Law of Sines.
  • SSA (Side-Side-Angle): Two sides and non-included angle. May have ambiguous case.

Formulas Used

  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Law of Cosines: a² = b² + c² - 2bc cos(A)
  • Heron's Formula: Area = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2
  • Area (SAS): Area = 0.5 × a × c × sin(B)

Examples

Example 1: SSS

Input: a = 5, b = 6, c = 7

Result: Area ≈ 14.70, Perimeter = 18

Example 2: SAS

Input: a = 5, B = 60°, c = 7

Result: b ≈ 6.24, Area ≈ 15.16

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