AAA Triangle Calculator

AAA stands for Angle-Angle-Angle, referring to a polygon where all three interior angles are known. The foundational rule governing any Euclidean triangle is that the sum of its interior angles always equals 180 degrees (or pi radians). Therefore, if you know any two angles, the third angle can be found using the equation: Angle3 = 180° - (Angle1 + Angle2). While AAA tells us the exact shape and proportions of a triangle, it does not define its absolute size, meaning infinitely many similar triangles can share the exact same three angles.

Imagine you are given a triangle where Angle 1 measures 45 degrees and Angle 2 measures 65 degrees, and you need to find the missing third angle. First, add the two known angles together: 45° + 65° = 110°. Next, subtract that sum from the total interior angle sum of a triangle, which is 180°. Calculating 180° - 110° reveals that Angle 3 equals 70°. Thus, your three interior angles are 45°, 65°, and 70°.

Always double-check that your known angles sum up to less than 180 degrees before calculating the third. Remember that an AAA designation proves similarity rather than congruence; knowing only the angles means the triangle can be scaled up or down infinitely without changing its shape. To find actual side lengths, you must combine AAA data with at least one known side length using the Law of Sines.