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.

- Triangle definition
- Hypotenuse
- Triangle interior angles
- Triangle exterior angles
- Triangle exterior angle theorem
- Pythagorean Theorem
- Proof of the Pythagorean Theorem
- Pythagorean triples
- Triangle circumcircle
- Triangle incircle
- Triangle medians
- Triangle altitudes
- Midsegment of a triangle
- Triangle inequality
- Side / angle relationship

- Perimeter of a triangle
- Area of a triangle
- Heron's formula
- Area of an equilateral triangle
- Area by the "side angle side" method
- Area of a triangle with fixed perimeter

- Right triangle
- Isosceles triangle
- Scalene triangle
- Equilateral triangle
- Equiangular triangle
- Obtuse triangle
- Acute triangle
- 3-4-5 triangle
- 30-60-90 triangle
- 45-45-90 triangle

- Incenter of a triangle
- Circumcenter of a triangle
- Centroid of a triangle
- Orthocenter of a triangle
- Euler line

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All rights reserved