30-60-90 triangle definition - Math Open Reference

30°- 60°- 90° Triangle

A right 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.

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This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is:

diagram of 30-60-90 right triangle showing sides are in the ratio 1, 2, root 3

The sides are always in the ratio 1 : 2 :

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.

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