AAA Triangle Calculator

Enter three angles of a triangle. Optionally provide one side length to fully determine the triangle.

Enter Angles

A=60° B=60° C=60° a b c
AAA alone determines the shape but not the size. All AAA triangles with the same angles are similar. Provide a side length below to determine a unique triangle.
Angles (degrees)
Known Side (optional)

Result

Enter three angles and click Calculate.

AAA Triangles: Similarity and Congruence

What is AAA?

AAA stands for "Angle-Angle-Angle." Since any triangle's angles sum to 180 degrees, knowing two angles automatically determines the third. AA (Angle-Angle) is sufficient to establish that two triangles are similar.

AAA and Similarity

Two triangles with the same three angles are similar -- they have the same shape but can differ in size. The corresponding sides are proportional:

a/d = b/e = c/f = k

Infinitely many triangles share the same three angles, each a scaled version of the others.

AAA Does Not Prove Congruence

For congruence (identical shape and size), at least one side must be known. Standard congruence conditions: SSS, SAS, ASA, AAS, and HL.

Using the Law of Sines

With one side known in addition to three angles, the law of sines uniquely determines the triangle:

a / sin(A) = b / sin(B) = c / sin(C)

Side Ratios

Even without a side, the ratio a : b : c = sin(A) : sin(B) : sin(C). For an equilateral triangle (60-60-60), the ratio is 1:1:1. For a 30-60-90 triangle, the ratio is 1 : √3 : 2.