Law of Cosines

\[c^2=a^2+b^2-2ab\cos(C)\]

a = triangle side a (m)

b = triangle side b (m)

c = triangle side opposite angle C (m)

C = included angle between sides a and b (rad or °)

The Law of Cosines is a trigonometric formula used to relate the lengths of the sides of a triangle with one of its angles.

It is an extension of the Pythagorean theorem for non-right triangles and allows the calculation of unknown sides or angles in any triangle.

Use the Law of Cosines when:

- Two sides and the included angle are known (SAS)

- Three sides are known and an angle must be calculated (SSS)

- Solving oblique triangles

- Working with distances and triangulation problems

It is especially useful when right triangle methods cannot be applied.

If:

a = 5 m

b = 7 m

C = 60°

Then:

c = √(5² + 7² - 2*5*7*cos(60°))

c = √(25 + 49 - 35)

c = √39

c ≈ 6.24 m

- Geometry and trigonometry

- Civil and mechanical engineering

- Surveying and mapping

- Navigation systems

- Physics calculations

- Computer graphics and 3D modeling

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