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# 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)

## Related Topics

• Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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## Citation

• Engineering ToolBox, (2013). Law of Cosines. [online] Available at: https://www.engineeringtoolbox.com/law-cosines-d_1857.html [Accessed Day Mo. Year].

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