Enter any combination of sides (a, b, c) and angles (A, B, C) of your scalene triangle — at least 3 values including one side — and get back the area, perimeter, all three sides, all three angles, and the triangle's altitudes. Works with SSS, SAS, ASA, AAS, and SSA configurations.
Area
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Perimeter
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Side a
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Side b
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Side c
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Angle A (°)
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Angle B (°)
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Angle C (°)
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Altitude h_a
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Altitude h_b
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Altitude h_c
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A scalene triangle is a triangle in which all three sides have different lengths and all three interior angles are different. Unlike equilateral triangles (three equal sides) or isosceles triangles (two equal sides), no sides or angles are the same in a scalene triangle.
The perimeter of a scalene triangle is simply the sum of its three sides: Perimeter = a + b + c. Since all sides are different lengths, you need to know (or calculate) all three side lengths first, then add them together.
There are several formulas. If you know the base and height: Area = 0.5 × base × height. If you know all three sides, use Heron's formula: Area = 0.25 × √((a+b+c)(−a+b+c)(a−b+c)(a+b−c)). If you know two sides and the included angle: Area = 0.5 × a × b × sin(C).
Each side of a triangle has a corresponding altitude. Once you know the area, you can find any altitude using: h_a = 2 × Area / a, h_b = 2 × Area / b, and h_c = 2 × Area / c. If you know two sides and the included angle, the height relative to side c is: h_c = a × sin(B).
You need at least 3 values including at least one side. Valid combinations are: SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the side between them), AAS (two angles and a non-included side), and SSA (two sides and a non-included angle — may have two solutions).
A scalene right triangle has one 90° angle and all sides of different lengths. Its area is simply: Area = 0.5 × leg₁ × leg₂, where leg₁ and leg₂ are the two shorter sides (not the hypotenuse). The hypotenuse can be found using the Pythagorean theorem: c = √(a² + b²).
The Law of Cosines states: c² = a² + b² − 2ab·cos(C). It is used when you know all three sides (SSS) to find angles, or when you know two sides and the included angle (SAS) to find the third side. It is a generalization of the Pythagorean theorem.
The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C). It is used when you know two angles and one side (ASA or AAS), or two sides and a non-included angle (SSA). It relates each side of a triangle to the sine of its opposite angle.