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Properties of a triangle formulas
16 formulas for Properties of a triangle, from the Trigonometry section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Angle sum | A + B + C = π 🧮 Solve step by step | |
| Sine rule | a/sin A = b/sin B = c/sin C = 2R 🧮 Solve step by step | R circumradius |
| Cosine rule | a² = b² + c² − 2bc cos A 🧮 Solve step by step | |
| Cosine rule (angle) | cos A = (b² + c² − a²) / 2bc 🧮 Solve step by step | |
| Projection rule | a = b cos C + c cos B 🧮 Solve step by step | |
| Tangent (Napier) rule | tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2) 🧮 Solve step by step | |
| Area | Δ = ½ bc sin A 🧮 Solve step by step | |
| Heron's formula | Δ = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 🧮 Solve step by step | |
| Circumradius | R = abc / 4Δ 🧮 Solve step by step | |
| Inradius | r = Δ / s = 4R sin(A/2) sin(B/2) sin(C/2) 🧮 Solve step by step | |
| Exradius | r₁ = Δ / (s − a) 🧮 Solve step by step | |
| Half-angle (sides) | sin(A/2) = √((s−b)(s−c)/bc) 🧮 Solve step by step | |
| Half-angle (sides) | cos(A/2) = √(s(s−a)/bc) 🧮 Solve step by step | |
| In any triangle | tan A + tan B + tan C = tan A tan B tan C 🧮 Solve step by step | |
| In any triangle | sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C 🧮 Solve step by step | |
| Median length | mₐ = ½ √(2b² + 2c² − a²) 🧮 Solve step by step |
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