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 |
Frequently Asked Questions
Enter three known properties (sides or angles) to calculate all missing side lengths, interior angles, perimeter, and area.
We use Heron's formula if three sides are known, or standard trigonometric area formulas (1/2 * a * b * sin C) for other cases.
The Law of Sines relates sides and angles of any triangle: a/sin(A) = b/sin(B) = c/sin(C).
📐 Find all angles and area from any 3 sides — Heron's Formula applied
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