30-60-90 Formulas

There are many types of triangles. Acute, Obtuse, Isosceles, Equilateral triangles. Out of these different triangles, few of them are special. When we say special, it means the sides and angles which are predictable and consistent.

Thirty sixty ninety triangle

Out of all the other shortcuts, 30-60-90 is indeed a special Triangle.

What is a 30-60-90 Triangle?

It is a triangle where the angles are always 30, 60 and 90. As one angle is 90, so this triangle is always a right triangle. As explained above that it is a special triangle so it has special values of lengths and angles.

The basic 30-60-90 triangle sides ratio is:
The side opposite the 30° angle x
The side opposite the 60° angle x * √3
The side opposite the 90° angle 2x

Example of 30 – 60 -90 rule

Example 1: Find the missing side of the given triangle.


As it is a right triangle in which the hypotenuse is the double of one of the sides of the triangle. Thus, it is called a 30-60-90 triangle where smaller angle will be 30. The longer side is always opposite to 60° and the missing side measures 3√3 units in the given figure.

Visit BYJU’S to learn other important mathematical formulas.