SSS Triangle Calculator

What Is an SSS Triangle?

An SSS triangle is fully defined by three side lengths (Side-Side-Side). The law of cosines finds all three interior angles, and Heron's formula gives the area.

SSS Formulas

Law of cosines for angle $\gamma$ opposite side $c$:

$$\cos \gamma = \frac{a^2 + b^2 - c^2}{2ab}$$

Heron's formula for area:

$$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2}$$

Worked Example

For sides 7, 8, and 9: $\gamma = \arccos((49+64-81)/112) \approx 73.40°$. Area $\approx 26.83$ square units.

Frequently Asked Questions

Are SSS triangles always congruent?

Yes. If all three sides of one triangle match another triangle's three sides, the triangles are congruent by the SSS criterion.

What if the sides violate the triangle inequality?

The sum of any two sides must exceed the third. Otherwise no triangle can be formed and our calculator will show an error.

How do I find angles from three sides?

Apply the law of cosines three times, once for each angle opposite each side.

Which area formula is used?

We use Heron's formula, which only requires the three side lengths and works for any valid triangle.

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What Is an SSS Triangle?

SSS Formulas

Worked Example

Frequently Asked Questions

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