# 30°- 60°- 90° Triangle

A triangle where the angles are 30°, 60°, and 90°.
Try this In the figure below, drag the orange dots on each vertex to reshape the triangle. Note how the angles remain the same, and it maintains the same proportions between its sides.

This is one of the 'standard' right triangles you should be able recognize on sight. (Another is the 45-45-90 triangle).

A fact you should commit to memory is:

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°). So while writing the ratio as 1: √3 :2  would be more correct, many find the sequence 1: 2: √3  easier to remember, especially when it is spoken. See also Side /angle relationships of a triangle. In the figure above, as you drag the vertices of the triangle to resize it, the angles remain fixed and the sides remain in this ratio.

## Corollary

If any triangle has its sides in the ratio 1 - 2 - √3, then it is a 30-60-90 triangle.
While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref