# Law of Cosines

## One side of a triangle when the opposite angle and two sides are known.

The "Law of Cosines" can be used to calculate one side of a triangle when the angle opposite and the other two sides are known.

The "Law of Cosines" can be expressed as

$$ c^2 = a^2 + b^2 - 2 a b cos C \tag{1} $$

*where *

*a, b and c = length of triangle sides (m, ft ..)*

*C = angle opposite side c (degrees)*

### Example - Calculate Side in Triangle

If side *a = 1 m*, side *b = 1.3 m* and angle *C = 60 degrees* - the side c can be calculated by modifying eq. 1 to

$$ c = \sqrt{ (1 m)^2 + (1.3 m)^2 - 2 (1 m) (1.3 m) cos (60 degrees) } = \underline{1.18} m $$

### Law of Cosines Calculator

The generic calculator below can used to calculate the side c:

*a (m, ft ....)*

*b (m, ft ....)*

*C (degrees)*