Triangle Calculator
Calculate area, perimeter, missing sides and angles for any triangle.
Triangle Properties
Quick Reference
Key Formulas
- Area: ½ × base × height
- Heron's: √[s(s-a)(s-b)(s-c)]
- Law of Cosines: c² = a² + b² - 2ab cos(C)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Solution Methods
- SSS: Three sides → Law of Cosines
- SAS: Two sides, included angle → Law of Cosines
- AAS/ASA: Two angles, one side → Law of Sines
- SSA: Two sides, non-included angle → Law of Sines
Understanding Triangle Properties
Triangles are fundamental geometric shapes with three sides and three angles. This calculator helps you solve for unknown sides and angles using mathematical relationships like the Law of Cosines, Law of Sines, and basic trigonometry.
Triangle Types
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Scalene: All sides have different lengths
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Isosceles: Two sides are equal in length
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Equilateral: All three sides are equal
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Right: One angle is exactly 90 degrees
Calculation Methods
Depending on the given values, different mathematical approaches are used:
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SSS (Side-Side-Side): All three sides known
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SAS (Side-Angle-Side): Two sides and included angle
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ASA/AAS: Two angles and one side
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SSA: Two sides and a non-included angle (ambiguous case)
Key Formulas
Area (Heron's Formula):
A = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2
where s = (a+b+c)/2
Law of Cosines:
c² = a² + b² - 2ab·cos(C)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Common Applications
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Engineering: Structural analysis and design
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Navigation: GPS and surveying calculations
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Architecture: Roof angles and space planning
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Physics: Force vectors and wave analysis
Tips for Accuracy
- • Enter at least one side length for valid calculations
- • Use π expressions for radians (e.g., π/3, 2π/5)
- • Check that angle sum equals 180° (or π radians)
- • Verify triangle inequality: sum of any two sides > third side
- • For SSA cases, be aware of potential ambiguous solutions