Pythagorus Theorem

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Pythagorus Theorem

For right-angled triangles, the Pythagorus Theorem lets us calculate a side length from any of the other two.

The Pythagorus Theorem is:

$a^2 + b^2 = c^2$

In the case of the 3, 4, 5 triangle (see previous section), then:

$3^2 + 4^2 = 5^2$
$9 + 16 = 25$

If we’re missing a side length, then we can use it to work backwards.

$x^2 + 4^2 = 5^2$
$x^2 + 16 = 25$
$x^2 = 9$
$x = 3$

If we look at a triangle whose hypotenuse is of length 1, the other two sides (going back to the SohCahToa) have a length of sinθ and cosθ. The Pythagorus Theorem gives us:

$\cos^2 \theta + \sin^2 \theta = 1$

This is known as the Pythagorean Identity. It relates sine and cosine to each other and is an important tool for manipulating and simplifying trigonometric equations.

Back up to Trigonometry

Proof

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Back up to Trigonometry

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