### Topic Page: Pythagorean theorem

**Pythagoras’ theorem**from

*The Penguin Dictionary of Science*

**Pythagoras' theorem**from

*The Hutchinson Unabridged Encyclopedia with Atlas and Weather Guide*

In geometry, a theorem stating that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. If the hypotenuse is h units long and the lengths of the other sides are a and b, then h^{2} = a^{2} + b^{2}.

The theorem provides a way of calculating the length of any side of a right-angled triangle if the lengths of the other two sides are known. For example, to find the length of a bridge constructed over a valley 120 m wide, when the vertical drop of the bridge is 20 m:

Using Pythagoras' theorem B^{2} = 120^{2} + 20^{2}, so B^{2} = 14,400 + 400 = 14,800, giving b = √14,800 = 121.66 (to two decimal places).

The length of the bridge is 121.66 m.

Pythagoras' theorem is also used to determine certain trigonometric identities such as sin^{2} θ + cos^{2} θ = 1.

essays

Mathematics

The Origins of Mathematics

Pythagoras' theorem: working out angles

At the Bottom of the Garden – Practical Use of Pythagoras' Theorem

It's That Man Again – Pythagoras and His Theorem

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Dave's Short Trig Course

Pythagoras' Theorem

SOS Mathematics: Trigonometry

Trigonometry

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