The Formulas Used
Heron's Formula — Area from 3 Sidess = (a + b + c) ÷ 2 (semi-perimeter)
Area = √[s(s−a)(s−b)(s−c)]
Example: a=3, b=4, c=5 → s=6
Area = √[6×3×2×1] = √36 = 6
Area = √[s(s−a)(s−b)(s−c)]
Example: a=3, b=4, c=5 → s=6
Area = √[6×3×2×1] = √36 = 6
Law of Cosines — Find Anglescos(A) = (b² + c² − a²) ÷ (2bc)
A = arccos[(b² + c² − a²) ÷ (2bc)]
A = arccos[(b² + c² − a²) ÷ (2bc)]
Triangle Inequality Rule
Not all combinations of three sides form a valid triangle. The Triangle Inequality Theorem states that the sum of any two sides must be greater than the third side:
- a + b > c
- a + c > b
- b + c > a
If this is violated, our calculator returns an error rather than incorrect results.
Types of Triangles
| Type | Condition | Example |
|---|---|---|
| Right Triangle | One angle = 90° | 3-4-5 triangle |
| Equilateral | All sides equal | a=b=c |
| Isosceles | Two sides equal | a=b≠c |
| Scalene | All sides different | a≠b≠c |
| Obtuse | One angle > 90° | Largest angle obtuse |
📐 Find all angles and area from any 3 sides — Heron's Formula applied
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