You learned it for a test. It quietly runs construction, GPS, screen sizes and architecture for the rest of your life.
There is a lot of jargon around this one. Strip it away and the math is genuinely simple. You learned it for a test. It quietly runs construction, GPS, screen sizes and architecture for the rest of your life.
55-inch TV = diagonal. With 16:9 ratio that's ~48" wide × 27" tall. Pythagoras under the hood.
Run + rise → rafter length: √(run² + rise²).
Distance from each satellite uses a 3D Pythagoras at planetary scale.
Stringer length = √(rise² + run²).
Football pitch diagonal = √(length² + width²) — useful in coaching drills.
Diagonal cable routing in stadiums and theatres.
Same diagonal can mean very different areas across aspect ratios.
Does it only work on right triangles? Yes — that's the whole point. For non-right triangles, use the law of cosines.
Why is √2 irrational? Pythagoras' own followers proved this and famously panicked. The square root of any non-perfect-square integer is irrational.
Whatever number you land on, sanity-check it against a second method or a quick estimate in your head.