How to Solve a Triangle
Solving a triangle means finding all the unknown missing values (sides and angles) based on the known values. This specific calculator operates on the SSS (Side-Side-Side) Postulate. If you know the lengths of all three sides of a valid triangle, there is only one mathematically possible shape it can take.
The Triangle Inequality Theorem
Not every combination of three numbers can form a triangle! The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side. If you try to enter sides of 2, 2, and 10, the calculator will give you an error because those lines could never physically connect to form a closed shape.
Calculating Area (Heron's Formula)
Most people learn the standard area formula: Area = ½ × Base × Height. But what if you don't know the height? Over 2,000 years ago, a mathematician named Hero of Alexandria created a formula to find the area using only the three sides.
Step 2 (Heron's Formula): Area = √(s × (s - a) × (s - b) × (s - c))
Calculating Angles (Law of Cosines)
To find the interior angles without knowing the height, we use trigonometry—specifically the Law of Cosines. It is a generalized version of the Pythagorean theorem that works for non-right triangles.