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.

Law of cosines

The "Law of Cosines" can be expressed as

c2 = a2 + b2 - 2 a b cos C                             (1)


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)

Law of Cosines - Excel Template

Law of cosines - excel template

Related Topics

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

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