Is this calculator free?

Yes, our calculator is completely free to use with no registration required.

Can I use it on mobile?

Yes, our calculator works perfectly on both mobile and desktop devices.

Updated: 2026-04-13

SSS Triangle Solver Tool

Overview: Calc-Tools Online Calculator offers a free and comprehensive suite of scientific and utility tools, including the specialized SSS Triangle Solver. This tool is designed to solve triangles where all three side lengths (SSS) are known. It automatically calculates the three internal angles using the law of cosines and determines the triangle's area, either through trigonometric formulas or Heron's formula. The calculator provides immediate results for area and perimeter upon entering the side lengths, simplifying a process that otherwise requires manual trigonometric computations. Furthermore, the article confirms a key geometric principle: all SSS triangles are congruent if their corresponding sides are equal. This makes the SSS Triangle Solver an efficient resource for students and professionals to verify solutions and understand triangle congruence.

Master SSS Triangles with Our Free Online Calculator. Whether your goal is to solve SSS triangles or understand the SSS congruence criterion, our free online calculator is the ideal starting point. This guide will explain the process of solving a triangle when you know all three sides, including calculating its internal angles and area.

Solving SSS Triangles: A Step-by-Step Guide

SSS stands for Side-Side-Side, meaning all three side lengths of the triangle are known. Follow this method to solve such a triangle.

First, apply the law of cosines to sides 'a' and 'b' to find the angle (γ) between them using the formula:
```
γ = acos((a² + b² − c²)/(2ab))
```
Next, apply the law of cosines again to sides 'a' and 'c' to determine the angle β.
The third angle, α, can then be found using the triangle sum theorem:
```
α = 180° - β - γ
```
To calculate the area, you can use the formula
```
Area = ½ ab sin γ
```
. Alternatively, Heron's formula is highly effective:
```
Area = √(s(s - a)(s - b)(s - c))
```
, where 's' represents the semi-perimeter, calculated as
```
s = (a + b + c)/2
```
.

Please note that computing the inverse cosine (acos) function typically requires a trigonometric table or specialized software. The simplest and most accurate solution is to use our dedicated SSS triangle solver.

How to Use Our Free SSS Triangle Calculator

Using our calculator is simple and straightforward. Just input the three known side lengths of your triangle into the designated fields. The tool will instantly compute and display all three interior angles, the area, and the perimeter. It's a fast and reliable free calculator designed for students and professionals.

Understanding SSS Triangle Congruence

Yes, SSS triangles are congruent based on the SSS postulate. If the three sides of one triangle are exactly equal in length to the three corresponding sides of another triangle, then the two triangles are congruent. This is a fundamental rule in geometry for proving triangle congruence.

Frequently Asked Questions

What is the standard area formula for an SSS triangle?

The most efficient formula is Heron's formula. For a triangle with sides a, b, and c, first calculate the semi-perimeter:

s = ½(a+b+c)

. Then, the area is given by:

Area = √(s(s-a)(s-b)(s-c))

Can you show an example calculation for a triangle with sides 2, 3, and 4?

Let's solve the triangle with sides a=2, b=3, c=4.

Find angle γ (between sides a and b):

γ = acos((2² + 3² - 4²)/(2 * 2 * 3)) ≈ 104.48°

Find angle β (between sides a and c):

β = acos((2² + 4² - 3²)/(2 * 2 * 4)) ≈ 46.57°

Find the final angle α:

α = 180° - 104.48° - 46.57° ≈ 28.95°

This demonstrates the complete solution using the law of cosines.

← Back to Formulas List