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Triangle Angles from Three Sides (Law of Cosines) — result sheet
All three interior angles of a triangle from its side lengths a, b, c.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A = arccos((b² + c² − a²) / 2bc), cyclically; angles in degrees sum to 180°.
The law of cosines inverts SSS congruence: each angle follows from the three sides. Inputs failing the strict triangle inequality are rejected instead of producing NaN angles.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side a — Opposite angle A.; minimum 1.0E-6; maximum 1000000000
- Side b — Opposite angle B.; minimum 1.0E-6; maximum 1000000000
- Side c — Opposite angle C.; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
A = 36.87°, B = 53.13°, C = 90°; largest side c.
Assumptions and limits
- Euclidean plane triangle; all sides use the same length unit.
- Strict triangle inequality: each pair of sides sums above the third.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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