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A quick, calm intro — then you choose when to climb.
In a right triangle, the two shorter sides are the legs (a and b). The longest side — always opposite the right angle — is the hypotenuse (c).
Legs (a, b) — the two shorter sides that meet at the right angle
Hypotenuse (c) — the longest side, always opposite the right angle
Pythagoras — — square both legs, add the squares, take the square root
Every step explained — why we do it, and what happens.
Why: Square both legs first — do not add the legs first. The legs are the two shorter sides meeting at the right angle.
What happens: 9 + 16 = c² — each leg squared.
Why: Add the squares of the legs: 3² = 9 and 4² = 16.
What happens: c² = 25 — the hypotenuse squared.
Why: Undo the square: take the square root of both sides.
What happens: c = 5 ✓ — the hypotenuse.
A ladder leans against a wall: its foot is 3 m from the wall and the top reaches 4 m up the wall. How long is the ladder?
Why: The ladder, the wall and the ground form a right triangle — the ladder is the hypotenuse, the longest side.
What happens: Legs 3 m and 4 m, hypotenuse c.
Why: Square the legs and add: 3² = 9, 4² = 16 — metres squared.
What happens: c² = 25 m².
Why: Root to undo the square: √25 = 5.
What happens: The ladder is 5 m ✓
Why: The glitch: adding the legs BEFORE squaring. Do not add the legs first — square each leg first. 3 + 4 = 7 would give c = 7 m, but the ladder is 5 m.
What happens: c = 5 m, not 7 m.
Why: Run the theorem backwards: 25 is 5², so the hypotenuse is 5. This is why 3-4-5 is a builder’s favourite triangle.
What happens: 5 m ✓ — the theorem holds.
Two classic glitches:
1.Adding the legs before squaring
Wrong:, so the hypotenuse is 7
Right:Square each leg first: , then .
2.Forgetting the square root
Wrong:, so
Right:Undo the square: .
You've got the concept! Let's lock it in with practice.
Learning is optional — the ladder is always open.