Analyze a triangle from three angles (AAA). Classify triangle type, compute side ratios, and fully solve when a side length is provided.
The AAA (Angle-Angle-Angle) condition specifies all three interior angles of a triangle. While knowing three angles alone does not determine a unique triangle — infinitely many similar triangles share the same angle triple — the angles tell you a great deal. You can classify the triangle as acute, right, or obtuse, and as equilateral, isosceles, or scalene. You can also compute the ratios of the sides using the Law of Sines, since side lengths are proportional to the sines of their opposite angles.
If you additionally provide one side length, the triangle becomes fully determined. The calculator then uses the Law of Sines to find all three sides, computes the area via Heron's formula, and derives the perimeter, inradius, and circumradius.
In practice, AAA problems arise when working with similar triangles: two triangles are similar if and only if their corresponding angles are equal. This is the AA (Angle-Angle) similarity criterion — since the third angle is forced when two are known, AAA reduces to AA. The concept is fundamental to trigonometry, surveying, and all branches of geometry. This calculator lets you enter two or all three angles, auto-computes the third, checks validity, classifies the triangle, and optionally solves for full dimensions when a side is given.
This aaa triangle calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Input Mode, Angle A, Angle B, Angle C and immediately see dependent measurements, validity checks, and geometry relationships in one place. That makes it easier to catch input mistakes early and confirm your final answer before moving to the next step.
Angle sum: A + B + C = 180° Side ratios: a/sin A = b/sin B = c/sin C (Law of Sines) Area (Heron): √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 Inradius: r = Area / s Circumradius: R = a / (2 sin A)
Result: For a=60, b=60, c=60, the tool returns the solved aaa triangle outputs shown in the result cards.
This example uses a realistic input set from the calculator workflow. After entry, the calculator applies the built-in aaa triangle formulas and reports derived values, checks, and classifications automatically.
This page is tailored to aaa triangle, with outputs tied directly to the form fields (Input Mode, Angle A, Angle B, Angle C). Instead of a one-line formula dump, it consolidates validation, derived metrics, and interpretation so you can solve and verify in one pass.
Use this tool for homework checks, worksheet generation, tutoring walkthroughs, and quick engineering geometry estimates. Presets and visual output blocks make it easier to compare scenarios and understand how each input affects the final result.
Keep units consistent, match each value to the correct field, and watch validity indicators before using the final numbers. If your case looks off, change one input at a time and use the output details to identify the mismatch quickly.
No. AAA defines the shape (all similar triangles share the same angles) but not the size. You need at least one side length to fix the triangle uniquely.
In Euclidean geometry the interior angles of a triangle always sum to 180°. If your inputs don't sum to 180°, the calculator flags the triangle as invalid.
The Law of Sines says a/sin A = b/sin B = c/sin C. So the side ratios are sin A : sin B : sin C.
Two triangles are similar if two pairs of corresponding angles are equal. Because the angle sum is 180°, the third pair is automatically equal — hence AA implies AAA.
No. Area requires at least one side length. With only angles you can determine the shape and side ratios, but not absolute dimensions.
A scalene triangle has all three sides (and all three angles) different. Compare with isosceles (two equal sides/angles) and equilateral (all equal).