Triangle Angle Calculator: Find All Angles from Sides or Other Angles (2026)
Calculate all angles of a triangle from side lengths or known angles. Use law of cosines, law of sines, or angle sum property.
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Put these formulas into practice with our instant, step-by-step Triangle Angle Calculator.
Finding the angles of a triangle is a fundamental skill in geometry. Whether you know three sides (SSS), two sides and an included angle (SAS), or two angles (AA), the triangle angle calculator finds all three angles using the law of cosines, law of sines, or angle sum property. Understanding these methods gives you the tools to solve any triangle problem.
Key Takeaway
The sum of angles in any triangle is always 180°. The law of cosines (cos(A) = (b² + c² - a²) / (2bc)) finds angles from three sides. The law of sines finds angles when you know a side and its opposite angle.
The Angle Sum Property
The most fundamental property of triangles is that the sum of all three interior angles is exactly 180° (or π radians). If you know two angles, the third is simply 180° minus the sum of the other two. This property applies to all triangles — scalene, isosceles, equilateral, right, acute, and obtuse.
The Law of Cosines
The law of cosines generalizes the Pythagorean theorem for all triangles. When C = 90°, it reduces to c² = a² + b². For any angle, it relates the cosine of the angle to the three sides. Use it when you know all three sides (SSS) or two sides and the included angle (SAS).
How to Use the Calculator
- Choose your input method: SSS, SAS, or AA.
- Enter the known values.
- The calculator finds all three angles with step-by-step derivations.
Frequently Asked Questions
- What is the sum of angles in a triangle?
- Always exactly 180° for any valid triangle in Euclidean geometry.
- Can a triangle have two right angles?
- No. Two 90° angles would leave 0° for the third angle, which is impossible.
- What is the ambiguous case (SSA)?
- When you know two sides and a non-included angle, there may be 0, 1, or 2 possible triangles.
Conclusion
Finding triangle angles is essential in geometry, surveying, and engineering. Use our free triangle angle calculator to solve any triangle with step-by-step explanations.