45-45-90 triangles: geometry math online learning
Posted By StudyGate
Lord of the 45-45-90 Triangle

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:

Right Triangles

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:

45-45-90 triangles: geometry math online learning

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
  • trigonometric functions



Pretty easy, huh?!

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

tangent of 45-45-90 triangle

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

Let’s recap!

45-45-90 triangle: geometry math online learning

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

sin cos tan in 45-45-90 triangle

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.