30°- 60°- 90° Triangle
A triangle where the angles are 30°, 60°, and 90°.
In the figure below, drag the orange dots on each
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:
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.
If any triangle has its sides in the ration 1 - 2 - √3, then it is a 30-60-90 triangle.
Related triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
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