For right-angled triangles, the Pythagorus Theorem lets us calculate a side length from any of the other two.
The Pythagorus Theor￼em is:
In the case of the 3, 4, 5 triangle (see previous section), then:
9 + 16 = 25
If we’re missing a side length, then we can use it to work backwards.
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 sinθ and cosθ. 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.