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by uk.co.hopi
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Right-angle triangle calculator

hopi_triangle_calculator
Read-onlyIdempotent

Solve a right-angle triangle from any two given values, at least one of which must be a side. Sides: a (opposite), b (adjacent), c (hypotenuse). angleA is angle A in degrees, between 0 and 90 (the third angle is the 90 degree right angle). Returns all three sides, both non-right angles, the area and the perimeter. Source: https://hopi.co.uk/triangle-calculator/

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aNoSide a, the opposite (greater than 0)
bNoSide b, the adjacent (greater than 0)
cNoSide c, the hypotenuse (greater than 0, must be the longest side)
angleANoAngle A in degrees, strictly between 0 and 90

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYes
bYes
cYes
areaYes
angleAYes
angleBYes
methodYes
summaryYes
perimeterYes
source_urlYesThe tool's page on hopi.co.uk (cite or open to check the figure)

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changed
    • addedOutput schema / required
      Added value: +[
+  "a",
+  "angleA",
+  "angleB",
+  "area",
+  "b",
+  "c",
+  "method",
+  "perimeter",
+  "source_url",
+  "summary"
+]
  2. First observed

TDQS

A4.5/5.0
Behavior4/5

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

Annotations already declare readOnlyHint=true and destructiveHint=false, covering safety. The description supplements this by detailing the full set of outputs (all sides, angles, area, perimeter) and referencing a source URL. This adds behavior context beyond annotations without contradicting them.

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 and front-loaded. The main purpose appears in the first sentence, followed by parameter definitions, outputs, and a source link. Every sentence contributes necessary information without redundancy or padding.

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

Completeness5/5

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

The description, combined with the exhaustive input schema and the presence of an output schema, provides complete information for an agent to select and call the tool correctly. It covers purpose, input requirements, and output expectations, leaving no critical gaps for a simple calculator.

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?

The input schema has 100% description coverage, providing per-parameter constraints by default. The description adds a cross-parameter rule not present in the schema: 'at least one of which must be a side.' It also clarifies the geometric roles of sides a, b, and c, which is essential for correct usage.

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 explicitly states 'Solve a right-angle triangle from any two given values, at least one of which must be a side,' clearly specifying the verb, resource, and core constraint. It also defines side roles and the angle. No other sibling tool handles triangle geometry, so differentiation is inherent.

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

Usage Guidelines4/5

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

The description provides clear input conditions: any two values with at least one side. It doesn't name alternatives or exclusions, but given the tool's unique function among siblings, this absence is acceptable. The prerequisite is explicit, which is the primary usage guidance.

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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