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title: How to Work with 30 60 90 Degree Triangles
---
## How to Work with 30 60 90 Degree Triangles

The 30-60-90 triangle is a special right triangle with angles of 30 degrees, 60 degrees, and 90 degrees. Because of this property of angles, the sides of the triangle are always in the following proportion:

Side opposite the 30° angle : Side opposite the 60° angle : Side opposite the 90° angle = <img src="https://latex.codecogs.com/svg.latex?$&space;1&space;:&space;\sqrt{3}&space;:&space;2&space;$" title="$ 1 : \sqrt{3} : 2 $" /> <br />

If it is mentioned that the given triangle is a 30-60-90 triangle and one of the sides is given then we can calculate the measures of other sides.

Consider a 30-60-90 triangle with the hypotenuse(side opposite to 90°) is 6. <br />
Then the measure of the side opposite to 30° is 3 and the measure of the side opposite to 60° is <img src="https://latex.codecogs.com/svg.latex?$&space;3\sqrt{3}&space;$" title="$ 3\sqrt{3} $" />

Similarly, we can calculate the measure of remaining sides when measure of one side is given.