Triangle Angle Finder
Use this calculator to find triangle angles with three common methods. All angle inputs and outputs are in degrees.
Rule used: A + B + C = 180°
Rule used: Law of Cosines
Rules used: Law of Cosines + angle sum of triangle
How to use this find angles in triangles calculator
This tool is designed to quickly calculate triangle angles from common known values. Whether you are solving homework, checking engineering dimensions, or reviewing geometry basics, this missing angle calculator gives fast and accurate results.
Start by selecting your input type: two known angles, three known sides (SSS), or two sides plus an included angle (SAS). Enter your values and click Calculate Angles. The calculator validates the triangle and then returns each angle.
Triangle angle rules used by the calculator
1) Angle sum rule
Every triangle has interior angles that add up to exactly 180°. If two angles are known, the third is:
C = 180° − A − B
2) Law of Cosines (for SSS and SAS)
When sides are known, angle values can be found with the law of cosines:
- cos(A) = (b² + c² − a²) / (2bc)
- cos(B) = (a² + c² − b²) / (2ac)
- cos(C) = (a² + b² − c²) / (2ab)
The calculator handles the inverse cosine conversion and includes numeric safety checks for stable output.
When to use each method
- Two Angles Known: Fastest method when two interior angles are given.
- Three Sides Known (SSS): Best when all side lengths are measured.
- Two Sides + Included Angle (SAS): Useful in surveying, drafting, and CAD sketches.
Worked examples
Example A: Missing third angle
Given A = 35° and B = 75°, the missing angle is:
C = 180° − 35° − 75° = 70°
Example B: Find all angles from sides
Given a = 6, b = 8, c = 10, the triangle is right-angled. The calculator returns approximately:
- A ≈ 36.87°
- B ≈ 53.13°
- C = 90°
Example C: SAS case
Given a = 9, b = 12, and included C = 40°, the calculator first finds side c using law of cosines, then computes A and B from the completed triangle.
Common mistakes to avoid
- Entering an angle of 0° or 180° (not a valid triangle angle).
- Using side lengths that violate triangle inequality (a + b must be greater than c, etc.).
- Mixing units for sides (all sides should use the same unit).
- Confusing the included angle in SAS with a non-included angle.
FAQ
Does this calculator work for obtuse triangles?
Yes. It supports acute, right, and obtuse triangles as long as the inputs define a valid triangle.
Are results rounded?
Yes. Outputs are rounded for readability (up to 4 decimal places) while calculations maintain internal precision.
Can I use this as a triangle angle checker?
Absolutely. It is useful for verifying hand calculations from geometry, trigonometry, and technical design problems.
Final notes
A reliable triangle angle finder saves time and reduces calculation errors. If you want to solve for unknowns quickly, this find angles in triangles calculator is a practical tool for students, teachers, and professionals alike.