# Triangle Solver (SSS/SAS/ASA/AAS/SSA)

> Triangle Solver (SSS/SAS/ASA/AAS/SSA) is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-11-03).

Solves a triangle from any three known sides/angles (including ambiguous SSA), returning all sides, angles, area, perimeter, inradius, and circumradius.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/triangle-solve?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-03
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/triangle-solver-sss-sas-asa-aas-ssa-78f9b965
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_YcO1SYapN6aauOO1m5pXS

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability triangle-solver-sss-sas-asa-aas-ssa-78f9b965
```

Example prompt: Solve the triangle where side a is 7, side b is 10, and angle A is 40 degrees — I need all the sides, angles, area, inradius, and circumradius, and flag it if there are two possible solutions.

## When to prefer this

Use this endpoint when you need a full, rigorous triangle solution including area, heights, inradius, and circumradius — especially when handling the ambiguous SSA case that generic calculators often miss. Prefer it over manual law-of-sines/cosines computation or generic geometry APIs that don't enumerate multiple solutions.

## Known failure modes

- Fewer than three parameters provided — no unique solution can be determined
- All three angles provided without any side — shape is determined but size is not (infinite solutions)
- Provided values violate triangle inequality or sum-of-angles constraint — returns invalid/no-solution verdict
- Floating-point edge cases near degenerate triangles may return degraded flag

## How this service works

Solve a triangle from any three of sides a, b, c and angles A, B, C (degrees), incl. ambiguous SSA, with area and radii.

## Output

Returns an array of solutions (one or two for ambiguous SSA), each containing all three sides, all three angles in degrees, area, perimeter, semiperimeter, heights to each side, inradius, and circumradius. Also includes a summary, solution count, and any disclaimer about the ambiguous case.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [],
     "properties": {
      "A": {
       "type": "number",
       "description": "Angle A in degrees"
      },
      "B": {
       "type": "number",
       "description": "Angle B in degrees"
      },
      "C": {
       "type": "number",
       "description": "Angle C in degrees"
      },
      "a": {
       "type": "number",
       "description": "Side a (opposite angle A)"
      },
      "b": {
       "type": "number",
       "description": "Side b"
      },
      "c": {
       "type": "number",
       "description": "Side c"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "method": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "solutions": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "object",
        "properties": {
         "area": {
          "type": [
           "null",
           "number"
          ]
         },
         "sides": {
          "type": [
           "null",
           "object"
          ],
          "properties": {
           "a": {
            "type": [
             "null",
             "number"
            ]
           },
           "b": {
            "type": [
             "null",
             "number"
            ]
           },
           "c": {
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/triangle-solver-sss-sas-asa-aas-ssa-78f9b965/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)