ASA Triangle Calculator — Angle-Side-Angle
Enter two angles (A and B) and the side between them (c) to solve the ASA (Angle-Side-Angle) triangle: get all three sides, the third angle, area, perimeter and height in one click.
°
°
Area = c² · sin(A) · sin(B) / (2 · sin(C))
- 1
Third angle C = 180° − A − B
180 − 50 − 60 = 70° - 2
sin(A), sin(B), sin(C)
sin(50°) = 0.766044, sin(60°) = 0.866025, sin(70°) = 0.939693 - 3
Area = c² × sin(A) × sin(B) ÷ (2 × sin(C))
10² × 0.766 × 0.866 ÷ (2 × 0.9397) = 35.2995
How does this calculator work?
Given angles A and B and included side c: third angle C = 180° − A − B; sides a = c·sin(A)/sin(C), b = c·sin(B)/sin(C) by the Law of Sines; Area = c²·sin(A)·sin(B)/(2·sin(C)). The triangle is uniquely determined whenever A + B < 180° and c > 0.
Formula
How this is calculated
The ASA (Angle-Side-Angle) case arises when you know two angles of a triangle and the length of the side that lies between them. Because all three angles of a triangle sum to exactly 180°, the third angle C is simply 180° minus the two known angles. This is the first and easiest step.
With three angles and one side known, the Law of Sines takes over: in any triangle the ratio of each side to the sine of the opposite angle is constant — a/sin(A) = b/sin(B) = c/sin(C). Rearranging gives a = c·sin(A)/sin(C) and b = c·sin(B)/sin(C), uniquely determining the missing sides.
The area follows from the two angles and the included side without needing an explicit height: Area = c² · sin(A) · sin(B) / (2 · sin(C)), a direct consequence of the general formula Area = ½·a·b·sin(C). All results are uniquely determined — unlike the ambiguous SSA case. Inputs must satisfy A + B < 180° and all values must be positive.
Frequently asked questions
Knowing two angles fixes all three angles (since they sum to 180°). Adding the length of the included side then sets the scale. The Law of Sines resolves the remaining sides uniquely. There is no ambiguity, unlike the SSA case where two solutions can exist.
ASA uses two angles and the side between them (included side). AAS (Angle-Angle-Side) uses two angles and a side not between them. Both uniquely determine the triangle, but the computation order differs: in AAS you first find the third angle, then use the Law of Sines with the non-included side.
Angles are in degrees; sides can be in any length unit (cm, m, inches, feet, etc.) as long as all sides use the same unit. The area will be in square units of whatever length unit you choose.
Also known as
TG we-Calculate Editorial Team. (2026). ASA Triangle Calculator — Angle-Side-Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/asa-triangle-calculator
TG we-Calculate Editorial Team. "ASA Triangle Calculator — Angle-Side-Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/asa-triangle-calculator.
TG we-Calculate Editorial Team, "ASA Triangle Calculator — Angle-Side-Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/asa-triangle-calculator
@misc{wecalculate_asa_triangle_calculator, title = {ASA Triangle Calculator — Angle-Side-Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/asa-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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