SSS Triangle Calculator

No 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!

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

1. Apply the law of cosines to sides a and b to determine the angle between these sides:
   γ = acos((a² + b² − c²)/(2ab))
2. Apply again the law of cosines to a and c to determine the angle β.
3. Compute the remaining angle as α = 180° - β - γ .
4. 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.

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.

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.

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!):

• AAA triangle;
• AAS triangle;
• SAS triangle;
• ASA triangle;
• Triangle area;
• Triangle congruence;
• Midsegment of a triangle;
• Circumcenter of a triangle;
• Acute triangle;
• Obtuse triangle;
• Oblique triangle; and
• Base of a triangle.

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).

1. 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°
2. 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°
3. Compute the remaining angle α as α = 180° - 104.48° - 46.57° = 28.95°.