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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.
(If there is no image below, see support page.)
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 : Square root of 3.

With the '2' being the hypotenuse (longest side). This ratio will come in handy later in the study of trigonometry. 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.

Also notice that the smallest angle is always opposite the smallest side.

Related triangle topics

General

Triangle types

Triangle centers

Congruence and Similarity

Triangle quizzes and exercises

(C) 2007 Copyright John Page