# SSS Triangle Calculator

Table of contents

How do I solve SSS triangles?How to use this SSS triangle calculator?Are SSS triangles congruent?Omni's triangle resourcesFAQsNo matter if you're interested in **solving SSS triangles** or rather want to learn about the **congruence of SSS triangles**, this SSS triangle calculator is the perfect place to start! We'll discuss:

- how to solve a SSS triangle, that is, how to
**determine the three internal angles**of the triangle; and - how to compute the
**area of an SSS triangle**.

With Omni's SSS triangle solver you'll become a sssuper triangle expert!

## How do I solve SSS triangles?

*SSS* means we know **all three sides of a triangle**. To solve an SSS triangle:

- Apply the
**law of cosines**to sides`a`

and`b`

to determine the angle between these sides:

`γ = acos((a² + b² − c²)/(2ab))`

- Apply again the law of cosines to
`a`

and`c`

to determine the angle`β`

. - Compute the remaining angle as
`α = 180° - β - γ`

. - If you wish to determine the
**area**, compute`Area = ½ ab sin γ`

or use the Heron formula:`Area=√(s(s - a)(s - b)(s - c))`

, where`s = (a + b + c)/2`

.

🙋 Computing `acos`

may be non-obvious, you'll need to use trigonometric resources or specialized software. Or, which is the best choice, use Omni's SSS triangle solver!

## How to use this SSS triangle calculator?

Using our SSS triangle calculator is pretty straightforward! Just **enter the data** you have (the lengths of the three sides of your triangle), and the **results will appear** immediately! For your convenience, the area and perimeter also get calculated by default.

## Are SSS triangles congruent?

**Yes!** If all three sides of one triangle have their lengths equal to the lengths of the corresponding three sides of another triangle, then these two triangles are congruent by the SSS triangle congruence criterion.

## Omni's triangle resources

Do you have some other data than the three side lengths? You may need one of the **other triangle criterions**, like, for instance, SAS, AAA, AAS! We've covered all of them (and more!):

### What is the formula for an SSS triangle area?

The quickest formula for the area of a triangle with sides `a`

, `b`

, and `c`

is the **Heron's formula**:

`Area=√(s(s-a)(s-b)(s-c))`

, where `s`

is the semi-perimeter of the triangle; that is one-half of its perimeter: `s = ½(a+b+c)`

.

### How do I calculate a SSS triangle with sides 2 3 4?

- Apply the
**law of cosines**to sides`2`

and`3`

to determine the angle between these sides:

`γ = acos((2² + 3² - 4²)/(2 × 2 × 3)) =104.48°`

- Apply the law of cosines again to sides
`a`

and`c`

to determine the angle`β`

between theses sides.

`β = acos((2² + 4² - 3²)/(2 × 2 × 4)) =46.57°`

- Compute the remaining angle
`α`

as`α = 180° - 104.48° - 46.57° = 28.95°`

.