Scalene Triangle Calculator
Calculate all properties of a scalene triangle: sides, angles, area, perimeter, and heights
Calculate Scalene Triangle
SSS: 3 sides | SAS: 2 sides + included angle | ASA: 2 angles + included side | AAS: 2 angles + any side
Triangle Properties
Enter triangle parameters to calculate properties
Example Calculation
Example: Scalene triangle with sides 3, 4, 5 cm
Given: a = 3 cm, b = 4 cm, c = 5 cm
Check if scalene: 3 ≠ 4 ≠ 5 ✓ (All sides different)
Triangle inequality: 3+4 > 5, 3+5 > 4, 4+5 > 3 ✓
Semi-perimeter: s = (3 + 4 + 5) / 2 = 6 cm
Area (Heron's): A = √[6×(6-3)×(6-4)×(6-5)] = √[6×3×2×1] = √36 = 6 cm²
Type: Right scalene triangle (3² + 4² = 5²)
Scalene Triangle Properties
All three sides have different lengths
All three angles are different
No lines of symmetry
No rotational symmetry
Can be acute, right, or obtuse
Formulas Used
Heron's Formula (Area)
A = √[s(s-a)(s-b)(s-c)]
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)
Height Formula
h = 2A / base
Understanding Scalene Triangles
What Makes a Triangle Scalene?
A scalene triangle is the most general type of triangle where all three sides have different lengths. This also means all three angles are different. Most real-world triangles are scalene.
Key Characteristics
- •No equal sides (a ≠ b ≠ c)
- •No equal angles (A ≠ B ≠ C)
- •Irregular shape with no symmetry
- •Can be classified as acute, right, or obtuse
Calculation Methods
SSS (3 Sides)
Use Law of Cosines to find angles, then Heron's formula for area
SAS (2 Sides + Included Angle)
Use Law of Cosines for third side, then Law of Sines for remaining angles
ASA/AAS (Angles + Side)
Use Law of Sines to find missing sides and angles
Triangle Classification by Angles
Acute Scalene
All angles < 90°
Most common type
Right Scalene
One angle = 90°
Satisfies Pythagorean theorem
Obtuse Scalene
One angle > 90°
Largest angle is obtuse