Triangle Angle Calculator

To find a missing angle in any triangle, use one of two facts: the angles sum to 180°, or the law of cosines relates each angle to the sides opposite it.

From Two Known Angles

The simplest case. The third angle is 180 minus the sum of the two known. If A = 30° and B = 80°, then C = 180 − 30 − 80 = 70°.

From All Three Sides (SSS)

Use the law of cosines: cos(A) = (b² + c² − a²) / (2bc). Then take the inverse cosine to get A in degrees. Repeat for B and C, or use 180 − A − B for the third angle.

Worked Example (Sides 5, 7, 8)

• cos(A) = (49 + 64 − 25) / (2 × 7 × 8) = 88 / 112 = 0.7857. A = arccos(0.7857) ≈ 38.21°
• cos(B) = (25 + 64 − 49) / (2 × 5 × 8) = 40 / 80 = 0.5. B = arccos(0.5) = 60°
• C = 180 − 38.21 − 60 = 81.79°

From One Side and Two Angles

Find the third angle by subtraction (sums to 180°). Then use the law of sines if you also need the missing sides: a / sin(A) = b / sin(B) = c / sin(C).

Special Angle Cases

• Right triangle: one angle is 90°. The other two add to 90°.
• Equilateral: all three angles are 60°.
• Isosceles: two angles are equal (opposite the equal sides).
• 30-60-90 and 45-45-90 are common reference triangles in trigonometry.

Use the Full Calculator

The Triangle Calculator handles every scenario described on this page. For the deeper math and worked examples, read the companion guide.