Triangle Angle Calculator
Find all three interior angles of any triangle from its side lengths using the law of cosines.
How it works
- 1Enter the three side lengths a, b, and c. They must be positive and satisfy the triangle inequality (any two sides must sum to more than the third).
- 2Angle A = arccos((b² + c² − a²) ÷ (2bc)); angle B follows the same form; angle C = 180° − A − B.
- 3If the sides cannot form a valid triangle, the outputs show — instead of a number.
Use cases
- Checking whether measured side lengths form an acute, right, or obtuse triangle before cutting materials.
- Verifying structural geometry in engineering or carpentry where angle accuracy matters.
- Solving trigonometry homework that starts from side-side-side (SSS) data.
Frequently asked questions
What is the law of cosines?
It generalises the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). Rearranged, C = arccos((a² + b² − c²) ÷ (2ab)), letting you find any angle from three sides.
Why does the calculator show — for my inputs?
The triangle inequality requires the sum of any two sides to strictly exceed the third. If a + b ≤ c (or any rotation), the sides cannot close into a triangle and the angles are undefined.
Do the three angles always sum to 180°?
Yes — in Euclidean geometry the interior angles of every triangle sum to exactly 180°. The tool derives A and B, then sets C = 180° − A − B to avoid rounding drift.
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