"use strict";

function round2(x) { return Math.round(x * 100) / 100; }

module.exports = {
  slug: "right-triangle-pythagoras",
  title: "Right triangle side by the Pythagorean theorem",
  deck_category: "geometry",
  description: "Computes the missing side of a right triangle (hypotenuse or a leg) given the other two sides.",
  inputs: [
    { name: "mode", type: "string", required: true, description: "Which side to solve for.", enum: ["find_hypotenuse", "find_leg"] },
    { name: "known_a", type: "number", unit: "length units", required: true, description: "For find_hypotenuse: one leg. For find_leg: the known leg.", min: 0 },
    { name: "known_b", type: "number", unit: "length units", required: true, description: "For find_hypotenuse: the other leg. For find_leg: the hypotenuse.", min: 0 }
  ],
  outputs: [
    { name: "result", unit: "length units", description: "The computed hypotenuse (find_hypotenuse) or leg (find_leg)." }
  ],
  steps: [
    "The Pythagorean theorem: for a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2.",
    "If mode is find_hypotenuse: c = sqrt(known_a^2 + known_b^2), where known_a and known_b are the two legs.",
    "If mode is find_leg: known_b is the hypotenuse and known_a is a leg; the missing leg = sqrt(known_b^2 - known_a^2). known_b must be greater than known_a.",
    "Round to 2 decimals."
  ],
  constants: [],
  sources: [
    { kind: "edition_page", value: "Euclid. Elements, Book I, Proposition 47.", title: "Elements, Book I, Proposition 47 (the Pythagorean theorem)", publisher: "Standard geometry reference", retrieved_utc: "2026-09-30T19:47:00Z", note: "Classical statement and proof of the Pythagorean theorem." }
  ],
  disclaimer: null,
  questionText(inputs) {
    if (inputs.mode === "find_hypotenuse") {
      return `What is the hypotenuse of a right triangle with legs ${inputs.known_a} and ${inputs.known_b}?`;
    }
    return `What is the missing leg of a right triangle with hypotenuse ${inputs.known_b} and one leg ${inputs.known_a}?`;
  },
  run(inputs) {
    const { mode, known_a, known_b } = inputs || {};
    if (mode !== "find_hypotenuse" && mode !== "find_leg") throw new Error("mode must be find_hypotenuse or find_leg");
    if (typeof known_a !== "number" || known_a <= 0 || typeof known_b !== "number" || known_b <= 0) {
      throw new Error("known_a and known_b must be positive numbers");
    }
    let result;
    if (mode === "find_hypotenuse") {
      result = Math.sqrt(known_a * known_a + known_b * known_b);
    } else {
      if (known_b <= known_a) throw new Error("known_b (the hypotenuse) must be greater than known_a (the leg)");
      result = Math.sqrt(known_b * known_b - known_a * known_a);
    }
    result = round2(result);
    return { answer: `${result.toFixed(2)}`, values: { result } };
  },
  examples: [
    {
      name: "worked example",
      inputs: { mode: "find_hypotenuse", known_a: 3, known_b: 4 },
      expected: { answer: "5.00" },
      check: "3-4-5 is the classic Pythagorean triple, independently known: 3^2+4^2=9+16=25=5^2."
    },
    {
      name: "test vector: find a leg",
      inputs: { mode: "find_leg", known_a: 5, known_b: 13 },
      expected: { answer: "12.00" },
      check: "5-12-13 is the classic Pythagorean triple, independently known: 13^2-5^2=169-25=144=12^2."
    }
  ]
};