Triangle Calculator
Calculate triangle properties including sides, angles, area, and perimeter using various input methods
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Triangle Fundamentals
A triangle is a polygon with three sides and three angles. The sum of all angles in any triangle always equals 180 degrees. Triangles are classified by their sides (equilateral, isosceles, scalene) and by their angles (acute, right, obtuse).
Law of Cosines
The Law of Cosines relates the lengths of a triangle's sides to the cosine of one of its angles. For a triangle with sides a, b, c and angle C opposite to side c: c² = a² + b² - 2ab·cos(C). This law is particularly useful when you know two sides and the included angle (SAS) or all three sides (SSS).
Law of Sines
The Law of Sines states that the ratio of any side of a triangle to the sine of its opposite angle is constant: a/sin(A) = b/sin(B) = c/sin(C). This law is helpful when you know two angles and one side (ASA or AAS) or two sides and a non-included angle (SSA).
Area Formulas
The most common formula for triangle area is (1/2) × base × height. However, there are other useful formulas: Heron's formula uses all three sides, the SAS formula uses two sides and the included angle [(1/2)ab·sin(C)], and for right triangles, you can use (1/2) × leg₁ × leg₂.
Triangle Types
By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal). By angles: Acute (all angles less than 90°), Right (one 90° angle), Obtuse (one angle greater than 90°).