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pythagorean_calc

Find the missing side of a right triangle using the Pythagorean theorem. Input the two known lengths and leave the unknown as zero.

Instructions

Solve Pythagorean theorem: find missing side of right triangle.

Parameters:
    a — Side a (leave 0 if unknown).
    b — Side b (leave 0 if unknown).
    c — Hypotenuse c (leave 0 if unknown).

Tool call template

This tool declares no required parameters. Add optional parameters from the input schema as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {},
    "name": "pythagorean_calc"
  }
}

Input Schema

Name	Required	Description	Default
`a`	No
`b`	No
`c`	No

Output Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

First observedv2.4.1Jun 22, 2026

TDQS

A3.5/5.0

Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries full burden. It only explains parameter roles but fails to disclose key behaviors such as validation (exactly two non-zero inputs required), error handling for invalid inputs, or output format. This lack of behavioral context hinders correct invocation.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is concise, front-loaded with the purpose, and presents parameters in a clear list format. Every sentence adds value without redundancy or unnecessary detail.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple mathematical tool, the description provides basic input semantics but omits important details such as the requirement that exactly one side must be unknown and validation rules. With an output schema existing, the output format is not critical but missing constraints reduce completeness.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, but the description explicitly defines each parameter: 'a — Side a (leave 0 if unknown)', etc. This adds meaning beyond schema titles and defaults, effectively compensating for the lack of structured descriptions.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool solves the Pythagorean theorem to find a missing side of a right triangle, which is a specific and distinct purpose. It names the verb 'solve' and the resource 'Pythagorean theorem', and the parameter explanation differentiates it from other calculation tools.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance is provided on when to use this tool versus alternatives like geometry_calc or quadratic_solver. There is no mention of prerequisites, exclusions, or context for using the tool.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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