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.

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30°- 60°- 90° Triangle

Corollary

Other triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises