30°- 60°- 90° Triangle

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.

Corollary

Other triangle topics

General

• 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 / Area

• 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

Triangle types

• 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

Triangle centers

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

Congruence and Similarity

• Congruent triangles

Solving triangles

• Solving the Triangle
• Law of sines
• Law of cosines

Triangle quizzes and exercises

• Triangle type quiz
• Ball Box problem
• How Many Triangles?
• Satellite Orbits