# 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.

 a = 2 b = 4 c = 5 Status = A = � B = � C = �

## 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.

 A = 49 � b = 4 c = 5 Status = a = � B = � C = �