And, finally, the side opposite the 90° angle will always be the largest side (the hypotenuse) because 90 degrees is the largest angle. The side opposite the 60° angle will be the middle length, because 60 degrees is the mid-sized degree angle in this triangle. The side opposite the 30° angle is always the smallest, because 30 degrees is the smallest angle. And the hypotenuse is 2 times the shortest leg, or $2√3$) (Why is the longer leg 3? In this triangle, the shortest leg ($x$) is $√3$, so for the longer leg, $x√3 = √3 * √3 = √9 = 3$. Because it is a special triangle, it also has side length values which are always in a consistent relationship with one another.įor example, a 30-60-90 degree triangle could have side lengths of:

So let's get to it!Ī 30-60-90 triangle is a special right triangle (a right triangle being any triangle that contains a 90 degree angle) that always has degree angles of 30 degrees, 60 degrees, and 90 degrees. In this guide, we'll walk you through what a 30-60-90 triangle is, why it works, and when (and how) to use your knowledge of it. And a 30-60-90 triangle-pronounced 'thirty sixty ninety'-happens to be a very special type of triangle indeed. Acute, obtuse, isosceles, equilateral…When it comes to triangles, there are many different varieties, but only a choice few that are 'special.' These special triangles have sides and angles which are consistent and predictable and can be used to shortcut your way through your geometry or trigonometry problems.

Altitude geometry example