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triangle_solve

Read-onlyIdempotent

Computes a triangle's angles, area, perimeter, inradius, circumradius, and type from three side lengths.

Instructions

Solve a triangle given three side lengths. Returns angles, area, perimeter, inradius, circumradius, and type.

Input Schema

NameRequiredDescriptionDefault
aYesSide a length.
bYesSide b length.
cYesSide c length.

Schema Changelog

Changes observed during successful MCP inspections.

  1. Addedv0.1.11

TDQS

A3.8/5.0
Behavior4/5

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

With no output schema, the description carries the return-value burden and does so explicitly (angles, area, perimeter, inradius, circumradius, type). Annotations already declare readOnly/idempotent/non-destructive, so the remaining gap is error behavior for degenerate inputs, which is unstated.

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?

Two sentences, front-loaded with the operation and followed by the return contract. No filler.

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

Completeness4/5

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

For a pure deterministic math tool with full schema coverage and annotations covering the safety profile, the description is nearly complete; only the invalid-triangle case is left implicit.

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

Parameters3/5

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

Schema description coverage is 100% and the parameters are self-evidently named a/b/c, so the schema does the heavy lifting. The description adds nothing about units, ordering constraints (a+b>c), or validation beyond restating 'three side lengths'.

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

Purpose4/5

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

States a specific verb and resource (solve a triangle) plus the exact input constraint (three side lengths) and the outputs produced. That is far more precise than the sibling geometry helpers like area_calculate or polygon_calculate, though it never names which sibling it replaces.

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

Usage Guidelines3/5

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

"Given three side lengths" implicitly defines the precondition, but there is no guidance on when to prefer this over area_calculate or polygon_calculate, and no note about what happens when the three lengths violate the triangle inequality.

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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