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Triangle Angle-Type Classifier — result sheet
Classify a triangle from its three side lengths and calculate its largest angle, perimeter, and semiperimeter.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Let c be the longest side. Compare c² with a²+b²: c² < a²+b² is acute, c² = a²+b² is right, and c² > a²+b² is obtuse. The largest angle is arccos((a²+b²−c²)/(2ab)).
A triangle's side lengths determine whether its largest angle is acute, right, or obtuse. The page validates that the three lengths can close into a triangle, then uses the longest side for the classification and law of cosines for the largest angle.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Side a — length units; minimum 1.0E-6; maximum 1000000000
- Side b — length units; minimum 1.0E-6; maximum 1000000000
- Side c — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Side a | 3 |
| Side b | 4 |
| Side c | 5 |
Right triangle; largest angle =90°; perimeter =12; semiperimeter =6.
Assumptions and limits
- The three inputs are positive lengths in one consistent unit.
- The triangle is Euclidean and planar.
- The side lengths must satisfy all strict triangle inequalities; a flat zero-area arrangement is rejected.
- The classification uses the longest side, with a small numerical tolerance for an equality at the right-triangle boundary.
- The largest angle is returned in degrees and is the angle opposite the longest side.
- Perimeter and semiperimeter use the same length unit as the inputs.
- The tool does not choose an orientation, coordinate placement, or measurement uncertainty.
- For measured sides close to the right-angle boundary, keep the original precision and inspect the unrounded inputs.
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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