Law of cosines

c^2=a^2+b^2-2ab\cos\gamma

Result unit: length units

What it describes

A generalization of the Pythagorean theorem to any triangle.

a, b, c

sides of the triangle

\gamma

angle between sides

a

and

b

A generalization of the Pythagorean theorem to any triangle. When

\gamma=90^\circ

\cos90^\circ=0

and the formula reduces to the Pythagorean theorem. It lets you find the third side from two sides and the angle between them.

A triangle with two sides and the included angle (or with three sides — finding an angle).

Given

a=3

b=4

\gamma=60^\circ

. Find side

c

Substitution

\cos60^\circ=0.5

Result

c^2=9+16-2\cdot3\cdot4\cdot0.5=13\Rightarrow c=\sqrt{13}\approx3.6

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