Triangle Calculator

Determining the geometric properties of non-right oblique triangles is essential in land surveying, roof truss engineering, carpentry layout, and coastal navigation. Users input the three positive side lengths (a, b, and c) of the target triangle. By relying on side-side-side (SSS) measurements, this approach eliminates the need to manually measure inaccessible interior angles or construct vertical altitude lines across irregular plots of land or physical structures.

The output displays the total enclosed surface area, total perimeter, semi-perimeter, and each of the three individual vertex angles expressed in degrees. Users can verify that all three interior angles sum to exactly 180 degrees. A vital practical caveat is the triangle inequality theorem: the sum of any two side lengths must be strictly greater than the third side length, otherwise the three segments cannot physically close to form a valid triangle.

The tool computes the semi-perimeter s = (a + b + c) / 2 and evaluates total area using Heron's formula, Area = √[s(s - a)(s - b)(s - c)]. Interior angles are derived by rearranging the law of cosines into cos A = (b² + c² - a²) / (2bc) and taking the inverse cosine. The final angle is determined by subtracting the first two angles from 180 degrees.