# Law of Cosines

## One side of a triangle when 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 (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 1 to

* c = ((1 m) ^{2} + (1.3 m)^{2} - 2 (1 m ) (1.3 m) cos(60 degrees))^{1/2}*

* = 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)*