What is Triangle Calculator?
Computes unknown sides, interior angles, semi-perimeter, and area of any triangle from three known dimensions using Heron's formula and the Law of Cosines.
How to Use This Calculator
- Enter the lengths of side a, side b, and side c.
- Ensure triangle inequality holds (a + b > c).
- View computed area, perimeter, and internal angles.
The Mathematical Formula & Variables
Heron's Formula: Area = sqrt(s * (s - a) * (s - b) * (s - c)) where s = (a + b + c) / 2
Step-by-Step Worked Example
Scenario: Triangle with sides a = 3, b = 4, c = 5.
- Semi-perimeter s = (3 + 4 + 5) / 2 = 6.
- Area = sqrt(6 * (6-3) * (6-4) * (6-5)) = sqrt(6 * 3 * 2 * 1) = sqrt(36) = 6.
Result: 6.000 sq units
Frequently Asked Questions
What is the triangle inequality theorem?
The sum of the lengths of any two sides of a valid non-degenerate triangle must be strictly greater than the length of the third side.