Triangles come in all sizes. Some are acute, some are obtuse, and some are *just right.*

The ones that are just right weren’t designed by Goldilocks. But she knew a right triangle when she saw it. She knew that a triangle was “right” when it had a 90° angle—perfect for drawing sharp corners. Like these:

But there was an even *more *special right triangles. She could hardly wait to contain herself when she saw it. It was the awesome **45 45 90 triangle**. Here it is in its mighty glory:

What’s so spectacular about this triangle? So many things it’s hard to list them all!

- The two sides making up the 90° angle have the
*same length* - The triangle is half of a square, as you can see on the right.
- That means its hypotenuse (the diagonal of the square) is the side x √2

Pretty easy, huh?!

- The
*tangent*of**45-45-90 triangles**is always 1.

Short of speaking with a trigonometry tutor for math homework help, it can’t get any easier than that!

*Let’s recap!*

The angles are easy to remember: 45+45+90 = 180°

The sides and hypotenuse are easy: the two sides are the same! x = x

The Hypotenuse is x√2

Goldilocks is a Lord of the **45-45-90 Triangles**.

*And now, you are, too!!!*

For more, check out our article about the half-angle formula.