Triangle Calculator (SSS / SAS)
A triangle is fully determined by three sides (SSS) or by two sides and the angle between them (SAS). Toolverge solves either case using the law of cosines to find the missing angle or side, then reports all three angles, the perimeter, and the area — using Heron's formula for the SSS case, since all three sides are already known.
How it works
- Choose SSS (three sides) or SAS (two sides plus the included angle).
- The law of cosines finds the missing angle or side.
- Perimeter and area are computed from the completed set of three sides.
Formula Law of cosines for angles/missing side; Heron's formula: area = √(s(s−a)(s−b)(s−c)), s = perimeter/2
Frequently asked questions
What is the area of a 3-4-5 triangle?
Using Heron's formula, the area is 6 square units — and since 3²+4²=5², it is also a right triangle.
What is the law of cosines?
A generalization of the Pythagorean theorem that relates the three sides of any triangle to the cosine of one of its angles.
Can any three side lengths form a triangle?
No. The sum of any two sides must be greater than the third (the triangle inequality), or no triangle exists.
What information does SAS need?
Two side lengths and the angle between them (the included angle), in degrees.
What is Heron's formula used for?
Finding a triangle's area from its three side lengths alone, without needing a height or angle.