Triangle Calculator
Calculate area, perimeter, angles, and heights from three side lengths (SSS)
Side Lengths
Triangle Area
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Perimeter (P)
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Angle A (α)
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Angle B (β)
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Angle C (γ)
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Semi-perimeter (s)
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Height on a (h_a)
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Height on b (h_b)
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Height on c (h_c)
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How to Use the Triangle Calculator
- Input Side Lengths: Enter positive numerical values for all three triangle sides ($a$, $b$, and $c$).
- Validate Triangle Inequality: Ensure the sum of any two side lengths is strictly greater than the third side length.
- Compute Properties: Click “Calculate Triangle” to compute total area, interior angles, heights, and classification.
Triangle Formulas
1. Heron’s Formula for Area:
s = (a + b + c) / 2
Area = sqrt[ s * (s – a) * (s – b) * (s – c) ]
Area = sqrt[ s * (s – a) * (s – b) * (s – c) ]
2. Law of Cosines for Interior Angles:
cos(A) = (b² + c² – a²) / (2 * b * c)
cos(B) = (a² + c² – b²) / (2 * a * c)
cos(C) = (a² + b² – c²) / (2 * a * b)
cos(B) = (a² + c² – b²) / (2 * a * c)
cos(C) = (a² + b² – c²) / (2 * a * b)
Frequently Asked Questions (FAQ)
What is the Triangle Inequality Theorem?
The Triangle Inequality Theorem states that for any valid non-degenerate triangle, the sum of lengths of any two sides must be strictly greater than the length of the remaining third side ($a + b > c$).
How are triangle classifications determined?
Triangles are classified by side congruence (Equilateral, Isosceles, Scalene) and by angle measures (Right-angled when one angle is $90^\circ$, Obtuse when one angle is $> 90^\circ$, Acute when all angles are $< 90^\circ$).
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