Right triangle
| Pythagorean | a² + b² = c² (hypotenuse c) |
|---|---|
| sin θ | = opposite / hypotenuse |
| cos θ | = adjacent / hypotenuse |
| tan θ | = opposite / adjacent |
| Area | = ½ · base · height |
Any triangle
| Law of sines | a / sin A = b / sin B = c / sin C = 2R (circumradius) |
|---|---|
| Law of cosines | c² = a² + b² − 2ab · cos C |
| Area (SAS) | = ½ · a · b · sin C |
| Area (Heron) | = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 |
| Sum of angles | A + B + C = 180° |
Solving strategies
| Given | Strategy |
|---|---|
| SSS (3 sides) | Law of cosines to find any angle; law of sines for others |
| SAS (2 sides + included angle) | Law of cosines for third side; law of sines for remaining angles |
| ASA / AAS | Sum of angles for third angle; law of sines for sides |
| SSA (ambiguous case) | Law of sines — may yield 0, 1, or 2 solutions |
Useful points
| Incenter | Intersection of angle bisectors — inscribed circle |
|---|---|
| Circumcenter | Intersection of perpendicular bisectors — circumscribed circle |
| Centroid | Intersection of medians — center of mass |
| Orthocenter | Intersection of altitudes |
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