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

Annotations already declare readOnlyHint, idempotentHint and a closed-world scope, so the safety profile is covered. The description goes beyond them by disclosing what the tool produces — exact radicals like 5√2, angles, area and 'full working' — which is meaningful because no output schema exists.

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?

Two compact sentences front-load the concrete example before the general formula, and nothing is redundant with the schema. The trailing marketing URL is mildly extraneous but does not obstruct selection.

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 (radicals, angles, area, full working). Combined with 100% parameter coverage in the schema and annotations that cover safety, an agent has what it needs to invoke it correctly; only explicit sibling routing is absent.

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 schema already documents a, b, c and the solve enum. The description reinforces the relationship between the inputs via the 3-4-5 example and the phrase 'any side', but adds no format or defaulting detail beyond the schema. Baseline 3 applies.

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?

The description states a specific verb and resource: solving a² + b² = c² for any side of a right triangle, plus the extras computed (radicals, angles, area). It does not explicitly distinguish itself from nearby siblings like triangle_calculator or square_root_calculator, but the formula-level specificity makes the tool's scope unmistakable.

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?

Usage is implied by the worked example (legs 3 and 4 → hypotenuse 5) and the 'solve for any side' phrasing, but there is no explicit when-to-use guidance, no exclusions, and no named alternative for non-right triangles or general triangle solving.

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