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 454590 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.
Corollary
If any triangle has its sides in the ration 1  2  √3, then it is a 306090 triangle.
Other triangle topics
General
Perimeter / Area
Triangle types
Triangle centers
Congruence and Similarity
Solving triangles
Triangle quizzes and exercises
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