# Cosine Law Calculator and Solver

Online calculator, based on the cosine Law , to solve triangle problems. The first calculator solves triangle problems when 3 sides are given (SSS case) and the second calculator solves triangle problems when 2 sides and their included angle are given (SAS case).

The cosine laws are given by:

1)

*a*^{ 2} = b^{ 2} + c^{ 2} - 2 b c cos(A)

which gives A = arccos [ (b^{ 2} + c^{ 2} - a^{ 2}) / 2 b c ]

2) *b*^{ 2} = a^{ 2} + c^{ 2} - 2 a c cos(B)

which gives B = arccos [ (a^{ 2} + c^{ 2} - b^{ 2}) / 2 a c ]

3) *c*^{ 2} = b^{ 2} + a^{ 2} - 2 b a cos(C)

which gives C = arccos [ (b^{ 2} + a^{ 2} - c^{ 2}) / 2 a b ]

## 1 - Use Cosine Law Calculator when 3 Sides are Given (SSS case)

Enter the 3 sides a, b and c as positive real numbers and press "enter". The outputs are the 3 angles A (opposite side a), B (opposite side b) and C (opposite side c) in DEGREES.

Note
For a triangle to exist, the sum of any two sides must be greater than the third side.

## 1 - Use Cosine Law Calculator when 2 Sides and the Included Angle are Given (SAS case)

Enter the given angle in A (in DEGREES) and the two sides in b and c as positive real numbers and press "enter". The outputs are side a and 2 angles B (opposite side b) and C (opposite side c) in DEGREES.

## More References and Links

Online Geometry Calculators and Solvers.

Sine Law Calculator and Solver.

Cosine Law Problems.

Sine Law Problems.

Laws of Sines and Cosines Problems Calculator.