The 306090 Triangle
A 306090 triangle is a special right triangle. The other type of special right triangle is 454590. These numbers represent the degree measures of the angles.


The reason these triangles are considered special is because of the ratios of their sides  they are always the same!
Special right triangles hold many applications in both geometry and trigonometry.
In this lesson you will learn the general formula for the ratios, and how to find missing sides of any 30 60 90 right triangle. We even offer a free study guide that easy explains the steps easily on one page! 
The General Formula of
a 306090 Triangle 


Giving the Sides their Special Names 
Before we explain how to find the missing sides, we need to give specific names to each of the sides. For example, the side across from the right angle is always called the hypotenuse (you probably already knew that from the pythagorean theorem). See below.
The side across from the 30° angle is known as the short leg (S.L.).
The side across from the 60° angle is known as the long leg (L.L.).
The side across from the 90° angle is known as the hypotenuse (Hyp.).
Important: Regardless of what direction the triangle is turned, the sides are still named according to their relationship to the angles.
Look at the examples below: The sides are always across from their angle
How to Find the Missing Side of a 306090 Triangle 
You will always be given one of the three sides. What you do from there depends on which side that you are given. Consider each case below.
Case #1: I know the Short Leg
 Find Hyp: Multiply by 2
 Find L.L: Multiply by Sqrt(3)
Case #2: I know the Hypotenuse
 Find S.L: Divide by 2
 Find L.L. Use Case #1
Case #3: I know the Long Leg
 Find S.L: Divide by Sqrt(3)
 Find Hyp: Use Case #1
Note: Always find S.L. first and then use Case #1! 


ownload GradeA's 306090 triangle study guide (.pdf)!
Examples: All Three Cases 
Case #1: I know the Short Leg
Case #2: I know the Hypotenuse
Case #3: I know the Long Leg
Learn about the other special right tirangle: 454590 triangle.
You may also be interest in other geometry formulas, or geometry help.
Or visit the GradeA homepage for more free math help.
