Solve an AAS triangle given two angles and a non-included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius.
The AAS (Angle-Angle-Side) configuration provides two angles and a non-included side of a triangle. Because the three interior angles must sum to 180°, two angles immediately determine the third. With all three angles known and one side given, the Law of Sines uniquely pins down the remaining two sides: a/sin A = b/sin B = c/sin C.
AAS is one of the classic triangle congruence and solving conditions. Unlike SSA (which can produce the ambiguous case), AAS always yields exactly one triangle. Once all sides are known, you can compute the full suite of triangle properties — area (via Heron's formula or the ½ab sin C formula), perimeter, semi-perimeter, the three altitudes, the three medians, the inradius (radius of the inscribed circle), and the circumradius (radius of the circumscribed circle).
This calculator takes angle A, angle B, and side a (opposite angle A), computes all derived quantities, and shows visual bar comparisons of sides and angles. It also provides a reference table of triangle types and presets for common configurations like the 30-60-90 and 45-45-90 triangles.
This aas triangle calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Angle A, Angle B, Side a (opposite Angle A), Decimal Places 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.
C = 180° − A − B b = a × sin B / sin A c = a × sin C / sin A Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 Height from vertex X: hₓ = 2 × Area / x Median to side a: mₐ = ½√(2b²+2c²−a²) Inradius: r = Area / s Circumradius: R = a / (2 sin A)
Result: For a=30, b=60, side=10, the tool returns the solved aas 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 aas triangle formulas and reports derived values, checks, and classifications automatically.
This page is tailored to aas triangle, with outputs tied directly to the form fields (Angle A, Angle B, Side a (opposite Angle A), Decimal Places). 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.
In AAS, the known side is not between the two known angles. In ASA, the known side is the one between (included by) the two known angles. Both uniquely determine the triangle.
No. AAS always gives exactly one triangle. The ambiguous case only arises with SSA (two sides and a non-included angle).
First solve for all sides using the Law of Sines, then use Heron's formula, or directly: Area = ½ × a × b × sin C. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
The inradius is the radius of the largest circle that fits inside the triangle (the incircle). It equals the area divided by the semi-perimeter.
The circumradius is the radius of the circle passing through all three vertices (the circumscribed circle). R = a / (2 sin A).
The Law of Sines relates each side to the sine of its opposite angle: a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius. Use this as a practical reminder before finalizing the result.