Math - Geometry

Pythagorean Theorem Explained Simply

The Pythagorean theorem describes a relationship between the three sides of a right triangle (a triangle with a 90° angle).

a² + b² = c² a and b are the legs (the two shorter sides at the right angle), c is the hypotenuse (the longest side, opposite the right angle)
a b c

If you know two of the three sides, you can calculate the third. Most often you want to find the hypotenuse c:

c = √(a² + b²)

💬 Mia asks Grandpa Theo

Mia

What do we actually need the Pythagorean theorem for in real life?

Grandpa Theo

For example, if you want to know how long a ladder needs to be to reach a window at an angle! Tradespeople use it all the time.

Mia

Can you show me an example to work through?

Grandpa Theo

Sure! Take a = 3 and b = 4. Then c² = 3² + 4² = 9 + 16 = 25, so c = 5. Almost every tradesperson knows the "3-4-5 triangle" by heart!

Mia

And does that work for every triangle?

Grandpa Theo

No, only for a right triangle - one with a real 90° angle. Without that, the formula doesn't work!

🎥 Want it explained in even more detail? There's a full video on our YouTube channel.

Watch video
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