Definition
A geometric rule stating that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. Written as a² + b² = c², where c is the hypotenuse.
Plain English
In any triangle that has one square corner, if you multiply each of the two shorter sides by itself and add the results, you get the same number you would get by multiplying the longest side by itself. This lets you find the length of any one side when you know the other two.
Context Anchor
Seen in aircraft maintenance math, layout work, measuring diagonals, and checking distances where two straight measurements meet at a square corner.
Derivation
Named after Pythagoras, a Greek mathematician from around 500 BC, who is credited with the first formal proof of the relationship. Knowing the name comes from a person, not a technical concept, helps the reader stop trying to decode the word itself.
Why Pilots Care
Supports precise measurements during structural repairs and component alignment to maintain airworthiness.
Analogy
Think of a square corner on a workbench. If you measure straight across one way and straight up the other way, the Pythagorean Theorem tells you the straight diagonal distance between the two far points.
Grounding Statement
Use this rule only when the two known sides meet at a true 90-degree corner.
Intuition Check
Do not use the Pythagorean Theorem for every triangle. It applies only to right triangles, where one corner is exactly 90 degrees.
Example Sentence 1
The technician used the Pythagorean Theorem to calculate the diagonal length of a rectangular access panel before cutting the replacement piece.
Example Sentence 2
During alignment checks, applying the Pythagorean theorem confirmed the proper diagonal distance across the horizontal stabilizer.