AAS Triangle Calculator
Two angles and a side that is not between them still fix a triangle exactly. Enter them for the remaining sides, the third angle and the area.
Once two angles are known the third follows from the 180° rule, and at that point every angle is known — so the side you have simply sets the scale through the law of sines.
How the aas triangle calculator works
Once two angles are known the third follows from the 180° rule, and at that point every angle is known — so the side you have simply sets the scale through the law of sines. AAS is never ambiguous, which is what separates it from SSA: knowing two angles pins the shape before any side is used.
Formula: a² = b² + c² − 2bc·cos A; a / sin A = b / sin B = c / sin C; area = ½ab·sin C
Worked examples
| Inputs | Area | Note |
|---|---|---|
| 35° and 65° with side a = 8 | 49.795 | the third angle is 80° |
| 90° and 30° with the side opposite 90° known | 21.6506 | a 30-60-90 triangle |
| A tall thin triangle | 9.4745 | most of the 180° is in the third angle |
FAQFrequently asked questions
What is the difference between ASA and AAS?
Only where the known side sits: between the two angles (ASA) or opposite one of them (AAS). Both are solved the same way and both give one answer.
Why is AAS not ambiguous when SSA is?
Because two angles fix the shape completely before any length is used; the side only sets the size.
Do I need the angle opposite my known side?
It helps but is not required — the third angle is always available from the 180° rule.
Can two angles alone solve a triangle?
They give the shape but not the size. Any one side is needed to set the scale.
What if my angles add to more than 180°?
Then no triangle exists, and the calculator says so rather than returning a wrong answer.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.