AAS Triangle Calculator (Angle-Angle-Side)
Enter two angles and the side opposite one of them to completely solve the triangle using the law of sines.
°
°
Found via law of sines: b = a sin B / sin A
- 1
Angle C = 180° − A − B
180° − 45° − 60° = 75° - 2
Law of sines ratio = a ÷ sin A
8 ÷ 0.7071 = 11.3137 - 3
Side b = ratio × sin B
11.3137 × 0.866 = 9.7980Law of sines: b / sin B = a / sin A.
How does this calculator work?
Given angles A and B and side a (opposite A), set C = 180° − A − B, then b = a sin B / sin A and c = a sin C / sin A via the law of sines. Area = ½ bc sin A, perimeter = a + b + c, circumradius = a / (2 sin A). The AAS case yields a unique triangle with no ambiguity.
Formula
How this is calculated
The AAS (Angle-Angle-Side) case occurs when you know two angles and the side opposite one of them — not the side between the two angles. Because the three angles of any triangle sum to 180°, the third angle follows immediately: C = 180° − A − B. Once all three angles are known, the law of sines provides a common ratio R = a / sin A, and the remaining sides are: b = R × sin B and c = R × sin C.
Area is computed from two sides and their included angle: area = ½ × b × c × sin A. This is equivalent to Heron's formula but avoids an extra square root. The circumradius of the triangle is a / (2 sin A), and the inradius is area / s where s = (a + b + c) / 2 is the semi-perimeter.
The AAS case always produces a unique triangle — there is no ambiguous case as with SSA. Inputs are rejected when any angle is zero or negative, when the two given angles sum to 180° or more (making C ≤ 0°), or when the side length is not positive.
Frequently asked questions
In AAS the known side is not between the two known angles — it is opposite one of them. In ASA the known side is the side between the two known angles. Both cases uniquely determine a triangle via the law of sines with no ambiguous solutions.
Yes — the labelling is conventional. Enter your two known angles in the A and B fields and the side opposite your first angle in "Side a". The calculator solves the full triangle regardless of which vertex letter you assign to each corner.
The third angle C = 180° − A − B would be zero or negative, which is impossible in a valid triangle. Make sure both angles are positive and their sum is strictly less than 180°.
Also known as
TG we-Calculate Editorial Team. (2026). AAS Triangle Calculator (Angle-Angle-Side) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/aas-triangle-calculator
TG we-Calculate Editorial Team. "AAS Triangle Calculator (Angle-Angle-Side)." TG we-Calculate. 2026. https://we-calculate.com/calculator/aas-triangle-calculator.
TG we-Calculate Editorial Team, "AAS Triangle Calculator (Angle-Angle-Side)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/aas-triangle-calculator
@misc{wecalculate_aas_triangle_calculator, title = {AAS Triangle Calculator (Angle-Angle-Side)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/aas-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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