Law of Cosines Calculator
Calculate the third side of a triangle using the Law of Cosines.
Triangle Visualization
Law of Cosines
The Law of Cosines is defined as:
\[ c^2 = a^2 + b^2 - 2ab\cos(C) \]
Where:
- a, b, c are the lengths of the sides of the triangle
- C is the angle between sides a and b
- c is the side opposite to angle C
Properties:
- Generalizes the Pythagorean theorem
- Works for any triangle (not just right triangles)
- When C = 90°, reduces to c² = a² + b² (Pythagorean theorem)
- Can be used to find any side or angle of a triangle
Applications:
- Navigation and surveying
- Physics (force vectors)
- Engineering (structural analysis)
- Computer graphics
- Astronomy
Common Cases:
- Acute triangles (C < 90°)
- Right triangles (C = 90°)
- Obtuse triangles (C > 90°)
- Equilateral triangles (a = b = c, C = 60°)
- Isosceles triangles (a = b)