Source: https://guthlabs.ai/docs/instruments/geometry-solver-triangle/implementation/

instrument implementation / implementation-contract

# Geometry Solver — Triangle implementation

A source-bound implementation contract for Geometry Solver — Triangle; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-with-binding-errata

**Evidence ID**: t4-153

**Effect**: Computation or source lookup only

## Input and validation requirements

The instrument reaches undefined behavior for zero-angle SSA input, must reject exact triangle-inequality degeneracy, and has a major unhandled unit-convention ambiguity for numeric angles. The convention vector also exposes inconsistent intermediate arithmetic: the correct degree SAS results are c=1.001826 and area=0.104714.

## Required corrections

````
[
  {
    "vector": 1,
    "field": "circumradius",
    "wrong": "2 cm",
    "correct": "2.5 cm",
    "cause": "working writes 60/24=2 (true 2.5)"
  },
  {
    "vector": 2,
    "field": "angles.A/B numeric",
    "wrong": "A≈43.945°, B≈76.055°",
    "correct": "A≈43.898°, B≈76.102°",
    "cause": "symbolic arccos(9/(2√39)) correct; numeric evaluation slipped"
  }
]
````

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "case": "SSS",
    "a": 3,
    "b": 4,
    "c": 5,
    "length_unit": "cm"
  },
  "expected_outputs": {
    "angles": {
      "A": "36.86989765°",
      "B": "53.13010235°",
      "C": "90°"
    },
    "area": "6 cm²",
    "perimeter": "12 cm",
    "altitudes": {
      "h_a": "4 cm",
      "h_b": "3 cm",
      "h_c": "2.4 cm"
    },
    "inradius": "1 cm",
    "circumradius": "2 cm",
    "classification": "right"
  },
  "working": "s=(3+4+5)/2=6. Heron area=√(6(6−3)(6−4)(6−5))=√(6×3×2×1)=√36=6 cm². Perimeter=3+4+5=12 cm. h_a=2K/a=2×6/3=4 cm; h_b=2×6/4=3 cm; h_c=2×6/5=2.4 cm. r=K/s=6/6=1 cm. R=abc/(4K)=(3×4×5)/(4×6)=60/24=2 cm. cos C=(a²+b²−c²)/(2ab)=(9+16−25)/(24)=0, so C=90°; A=arcsin(3/5)=36.86989765° and B=90°−A=53.13010235°."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/geometry-solver-triangle/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/geometry-solver-triangle/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/geometry-solver-triangle/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `tranche errata record`