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

With no annotations, the description carries full burden, and it does disclose one real operational trait beyond the schema: the tool is metered/paid and requires a signed wallet (5 free calls). It says nothing about error behavior when inputs are invalid (leg ≥ hypotenuse, non-numeric), precision of the result, or the shape of the return value.

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?

One tight sentence front-loads the operation, followed by a short trial-call note. The emoji and promotional framing add a little noise but cost nothing in comprehension.

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?

For a simple two-input math tool this is nearly sufficient, but with no annotations, no output schema, and no parameter descriptions, the agent is left guessing at input encoding (string vs number) and at what the returned leg looks like. A single clause on format and return value would close the gap.

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 coverage is 0%, so the description is the only source of parameter meaning — and "from the hypotenuse and the other leg" does successfully map the two parameters to their geometric roles. However, both parameters are typed as strings with no format guidance (decimal string? units? precision?), which is a meaningful gap for a numeric tool.

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?

"Returns the missing leg from the hypotenuse and the other leg" gives a concrete verb (returns) and a specific computed resource (the unknown leg), which is enough to distinguish it from a general triangle helper. It never names the sibling x402-pythagorean, so the agent must infer that this is the inverse operation rather than the hypotenuse solver.

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?

There is no statement of when to use this versus x402-pythagorean or any other geometry tool, and no preconditions (e.g. hypotenuse must be the larger value). The only extra sentence is about free trial calls, which is pricing, not usage guidance.

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