Random Triangle Set Generator

Generate nondegenerate triangles with side lengths, areas, and perimeters.

Description

Generate triangle side sets by sampling two sides and an included angle, then calculate area and perimeter.

Two positive sides and an included angle strictly between zero and 180 degrees determine a nondegenerate triangle. The law of cosines gives the opposite side; area can be obtained from the included angle and side lengths.^[1]

This generator samples two sides and an angle, then returns sideA, sideB, sideC, area, and perimeter for each triangle inside result.triangles. Side lengths share your chosen length unit; perimeter uses that unit and area uses its square. No coordinate vertices or angles are returned.

When to use Random Triangle Set Generator

Use it to create triangle-measurement exercises or geometry fixtures with calculated side, area, and perimeter values.

How to use Random Triangle Set Generator and understand its results

Enter shapeCount as an integer from 1 through 256 and positive maximumSideLength no greater than 10^100 in a consistent length unit.
Run the generator and read result.triangles, preserving the shared unit convention.
Use the side lengths and computed measurements in the intended exercise, and round only for display rather than before checking triangle relationships.

a,b = M × (0.1 + 0.9 × randomDraw); θ = π/6 + randomDraw × 2π/3

Each triangle consumes three draws. The first two sides lie from 0.1M inclusive toward M exclusive; the angle lies from 30° inclusive toward 150° exclusive.

c = sqrt(a² + b² − 2ab cos θ); area = a × b × sin θ / 2; perimeter = a + b + c

The implementation computes height b sin θ, uses the triangle-area calculator, and calls the triangle-perimeter tool.

json

{
  "input": {
    "shapeCount": 3,
    "maximumSideLength": 10
  },
  "randomDraw": 0.25,
  "output": {
    "result": {
      "triangles": [
        {
          "area": 4.573696663736567,
          "perimeter": 9.75,
          "sideA": 3.25,
          "sideB": 3.25,
          "sideC": 3.2500000000000004
        },
        {
          "area": 4.573696663736567,
          "perimeter": 9.75,
          "sideA": 3.25,
          "sideB": 3.25,
          "sideC": 3.2500000000000004
        },
        {
          "area": 4.573696663736567,
          "perimeter": 9.75,
          "sideA": 3.25,
          "sideB": 3.25,
          "sideC": 3.2500000000000004
        }
      ]
    }
  }
}

The bound applies to the two sampled sides, not to every output side: sideC can exceed maximumSideLength. With a and b near the bound and an obtuse angle, c approaches almost twice the bound. Invalid draws, nonpositive bounds, and out-of-range counts fail.

Limitations and assumptions

The default source is Math.random; no seed input or cryptographic entropy guarantee is provided. Repeated runs may select the same result, and the distribution depends on the random source.

The sampling is not uniform over triangle shapes, side triples, areas, or angles outside the chosen range. Repeated triangles are allowed.

Extremely small bounds can underflow squared lengths; large or very small inputs may lose numerical precision or fail downstream validation. The tool does not supply vertices, labels, or a rendered diagram.

Alternative or Complementary methods

Use the individual measurement tools to check a chosen triangle rather than generate one. A right-triangle calculator answers a constrained geometry problem with different inputs.

References

Precalculus 2e: Non-right Triangles and the Law of Cosines — OpenStax, Rice University

Similar or alternative tools

Triangle Area
Calculate area from an explicit base and perpendicular height.
Triangle Perimeter
Calculate perimeter from three supplied side lengths.