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# Law of Cosines

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:

## Related Topics

### • Mathematics

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