What this calculator does
Triangle angle questions usually use the 180° angle sum rule or the law of cosines.
Ways to find missing triangle angles
| Known values | Method | Notes |
|---|---|---|
| Two angles | C = 180° − A − B | The simplest case |
| Three sides | Law of Cosines | Find A, B, and C from side lengths |
| Right triangle side ratio | Inverse trig functions | Use arctan, arcsin, or arccos depending on known sides |
| One angle and two sides | Law of Sines or Law of Cosines | Depends on whether the angle is included |
Example: find the third angle
If two angles are 50° and 65°, the missing angle is 180° − 50° − 65° = 65°. This works for every triangle because the three interior angles always add to 180°.
Example: find angles from three sides
If all three side lengths are known, use the law of cosines. For angle A, the formula is cos(A) = (b² + c² − a²) / (2bc). The calculator repeats the same idea for angle B and angle C, then checks that the angles add to approximately 180°.
Angle type interpretation
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