Triangle Side–Angle Calculator — AAS & ASA Solver
Know two angles of a triangle and one side? Enter them here — the Law of Sines finds every remaining side and angle, plus area and perimeter, in one step.
Known combination
°
°
Third angle = 180° − A − B (triangle angle-sum theorem)
- 1
Sum of known angles A + B
45° + 60° = 105° - 2
Missing angle C = 180° − (A + B)
180° − 105° = 75°Interior angles of every triangle sum to exactly 180°.
How does this calculator work?
Two angles A, B and one side determine a unique triangle. The third angle is C = 180°−A−B. Then a/sin A = b/sin B = c/sin C gives every missing side. AAS: the known side is opposite angle A; ASA: it is enclosed between A and B. Enter the values to get all sides, angles, area and perimeter.
Formula
How this is calculated
The Law of Sines states that in any triangle the ratio of each side to the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C = 2R (where R is the circumradius). When two angles are known, the third angle follows immediately from the angle-sum theorem: C = 180° − A − B. This gives all three angles without knowing any sides.
With both the complete angle set and one known side, the common ratio a/sin A (or equivalently b/sin B or c/sin C) is determined, and each unknown side is simply ratio × sin(opposite angle).
AAS mode: you know angles A and B and the side a opposite to A. ASA mode: you know angles A and B and the side c that lies between them (c is the side opposite to the third angle C). Both modes produce a unique, unambiguous solution — unlike SSA which can yield two solutions. The calculator guards against impossible inputs (angle sum ≥ 180°) and returns a warning if the data is inconsistent.
Frequently asked questions
In AAS (Angle-Angle-Side) the known side is NOT between the two known angles — it is opposite to one of them. In ASA (Angle-Side-Angle) the known side IS between the two known angles. Both give a unique triangle; only the position of the known side differs.
Two angles fix the shape (all angles are known) but not the size — infinitely many triangles share the same angles (similar triangles of different scales). One side length fixes the scale, which is why you need at least one side alongside the angles.
The sine ratio (a/sin A = b/sin B = c/sin C) is the common constant of the Law of Sines for this triangle. It equals twice the circumradius (radius of the circle passing through all three vertices).
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Side–Angle Calculator — AAS & ASA Solver [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-side-angle-calculator
TG we-Calculate Editorial Team. "Triangle Side–Angle Calculator — AAS & ASA Solver." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-side-angle-calculator.
TG we-Calculate Editorial Team, "Triangle Side–Angle Calculator — AAS & ASA Solver," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-side-angle-calculator
@misc{wecalculate_triangle_side_angle_calculator, title = {Triangle Side–Angle Calculator — AAS & ASA Solver}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-side-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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