How this calculator works
Each interior angle must be positive and their sum must be 180 degrees. The sine rule then fixes b/a and c/a without choosing a length unit. The sample table rescales that shape: multiplying all sides by k multiplies its area by k². Its lengths are examples, not measurements inferred from the angles.
Formula
C = 180° - A - B; b/a = sin(B)/sin(A); c/a = sin(C)/sin(A); area/a² = (b/a)(c/a)sin(A)/2.
Worked example
Angles 30°, 60° and 90° give side ratios 1:√3:2. If a is later measured as 2 m, the sides become 2 m, 2√3 m and 4 m and the area is 2√3 m².
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Frequently asked questions
Can AAA determine actual side lengths?
No. A tiny triangle and a large triangle can have the same three angles. Measure one side to set the scale, then use AAS or ASA.
Why display area divided by a squared?
It is independent of size. Multiply that number by the square of your measured side a to obtain area in the corresponding square unit.
Can the three angles add to 179 degrees?
A plane triangle requires 180 degrees. This tool allows only a very small numerical tolerance for conversion roundoff, not measurement error.