## Pythagorus Theorem

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

The Pythagorus Theor￼em is:

a2 + b2 = c2

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

32 + 42 = 52

9 + 16 = 25

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

x2 + 42 = 52

x2 + 16 = 25

x2 = 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 sin*θ* and cos*θ*. The Pythagorus Theorem gives us:

￼

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.

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