Calculate all angles of a triangle when all three side lengths (SSS) are known.
Triangle Sides
Triangle Properties
6.00
Area (Heron's)
Angles calculated using the Law of Cosines.
Angle A36.9°
Angle B53.1°
Angle C90.0°
About this calculator
The SSS Case
When all three side lengths of a triangle are known, we can uniquely determine the measure of all three internal angles using the Law of Cosines. This is one of the most stable cases in trigonometry as there is no ambiguity.
💡
Pro Tips
The sum of any two sides must be strictly greater than the third side (Triangle Inequality).
The largest angle is always opposite the longest side.
The area is most efficiently calculated using Heron's Formula in this case.
!
Fun Facts
"SSS is a fundamental congruence theorem in geometry."
"Rigid structures like bridges use triangles because SSS forces a fixed shape that can't be deformed without changing side lengths."
"Heron of Alexandria, who created the area formula used here, was also a pioneer in steam power."
