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

Annotations cover safety (readOnly, idempotent, closed-world), and the description adds genuinely useful behavior: the full set of return values (other three parts, area, perimeter, type, scale drawing) and the warning that the SSA case is ambiguous. It does not say how the ambiguous case is resolved or what form the scale drawing takes.

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

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

Three short sentences, front-loaded with the capability and the returned values. The trailing web-page URL is not strictly necessary for tool invocation, keeping it just short of fully earned conciseness.

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

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

With no output schema, the description carries the burden of describing returns and does so competently by listing the derived outputs. The main residual gap is the ambiguous SSA case (single vs. two solutions) and the nature of the scale drawing output.

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

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

Schema description coverage is 100%, so the parameter meanings and the mode enum are already documented structurally. The description only restates the case abbreviations that map to the mode enum and the 'three parts' idea, adding no unit, ordering, or incompatibility guidance beyond the schema.

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

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

States a specific verb+resource: solve a triangle from three known parts and return the remaining parts plus area, perimeter, type and a scale drawing. That is enough to distinguish it from area_calculator or pythagorean_theorem_calculator in intent, but no sibling is named explicitly, so it stops short of a 5.

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

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

The opening question ('Know three parts of a triangle?') establishes the entry condition, and enumerating SSS/SAS/ASA/AAS plus the SSA ambiguous case tells the agent which input configurations are legitimate. There is no explicit when-not or named alternative, but the context is clear.

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