This formula comes from the law of cosines and solves an angle from the three side lengths. Repeating the formula for each side gives all angles, and the results should add to 180 degrees.
⚠All side lengths must be positive and satisfy the triangle inequality. Results are shown in degrees.
How Triangle Angle Calculation Works
Each angle is opposite its matching side. A longer side creates a larger opposite angle, and the law of cosines converts the three side lengths into angle measures.
SSS Input
The tool needs all three side lengths.
Opposite Pairing
Side a is opposite angle A.
Angle Sum
The three angles total 180 degrees.
Validation
Invalid side sets are rejected before calculation.
💡 Example: For sides 5, 6, and 7, the angles are about 44.415°, 57.122°, and 78.463°.
Applications of Triangle Angles
SSS TrianglesSurveyingRoof LayoutTrigonometry
Frequently Asked Questions
What is a triangle angle calculator?▼
It calculates the three angles of a triangle when all three side lengths are known.
What formula finds angles from sides?▼
The calculator uses the law of cosines, such as A = cos⁻¹((b²+c²-a²)/(2bc)).
How do I use this calculator?▼
Enter the three side lengths and click Calculate to get angles A, B, and C.
What if the sides cannot make a triangle?▼
The calculator checks the triangle inequality and shows an error if the sides are invalid.
Where are triangle angles from sides used?▼
They are used in construction, surveying, trigonometry, navigation, and geometry assignments.
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