Solve an ASA triangle given two angles and the included side. Compute all sides, area, perimeter, heights, medians, inradius, and circumradius.
The ASA (Angle-Side-Angle) condition provides two angles and the side between them (the included side). Since the three angles sum to 180°, knowing two immediately gives the third. With all three angles and one side known, the Law of Sines determines the remaining two sides: a/sin A = b/sin B = c/sin C. ASA is one of the four fundamental triangle congruence conditions (along with SSS, SAS, and AAS), and it always produces a unique triangle.
Once the triangle is fully determined, you can compute a wealth of properties. The area can come from Heron's formula or from the direct formula ½ab sin C. The three altitudes (heights) are each equal to 2 × Area divided by the base. The three medians follow from the formula mₐ = ½√(2b²+2c²−a²). The inradius — the radius of the inscribed circle tangent to all three sides — equals Area / s, where s is the semi-perimeter. The circumradius — the radius of the circumscribed circle through all three vertices — equals a/(2 sin A).
This calculator takes angle A, the included side c, and angle B, then solves the triangle completely. It displays visual bar charts comparing sides and angles, a heights-and-medians table, and an expandable reference of key triangle formulas.
This asa triangle calculator reduces manual rework when you need quick checks for assignments, exam prep, and design calculations. You can enter Angle A, Side c (included side, between A and B), Angle B, 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 a = c × sin A / sin C b = c × sin B / sin C Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2 Height hₐ = 2 × Area / a Median mₐ = ½√(2b²+2c²−a²) Inradius r = Area / s Circumradius R = a / (2 sin A)
Result: For a=30, c=10, b=60, the tool returns the solved asa 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 asa triangle formulas and reports derived values, checks, and classifications automatically.
This page is tailored to asa triangle, with outputs tied directly to the form fields (Angle A, Side c (included side, between A and B), Angle B, 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 ASA, the known side is between the two known angles (the included side). In AAS, the known side is not between the two angles. Both uniquely determine the triangle.
Two angles fix the shape (AA similarity), and the included side fixes the size. Together they uniquely determine the triangle up to congruence.
First find all sides via the Law of Sines, then use Heron's formula, or directly: Area = ½ × c² × sin A × sin B / sin C. Understanding this concept helps you apply the calculator correctly and interpret the results with confidence.
The included side is the side that lies between the two given angles. In ASA with angles A and B, the included side is c, which connects the vertices of A and B.
Yes. If one of the angles is 90°, ASA still works. For example, A = 30°, c = 10, B = 60° gives a 30-60-90 right triangle.
SSS (three sides), SAS (two sides + included angle), ASA (two angles + included side), AAS (two angles + non-included side), and HL (hypotenuse-leg for right triangles). Use this as a practical reminder before finalizing the result.