# The Law of Cosines - practice problems - page 2 of 4

The law of cosines is a mathematical formula used in trigonometry that relates the sides of a triangle to the cosine of one of its angles. Specifically, it states that in any triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:

c2 = a2 + b2 - 2ab * cos(C)

where c is the length of the side opposite angle C, a is the length of the side opposite angle A, and b is the length of the side opposite angle B. The formula is also known as "cosine formula" or "cosine rule".

The law of cosines can be used to find the length of a side of a triangle when the lengths of the other two sides and the angle opposite the unknown side are known. It can also be used to find an angle of a triangle when the lengths of all three sides are known.

It is particularly useful in solving triangles that are not right triangles, where the Pythagorean theorem can not be applied.

The law of cosines can also be useful in solving problems involving distance and navigation, like finding the distance between two points on the surface of the earth, or finding the distance between two celestial bodies. It is also used in physics and engineering, such as in calculating the force required to bend a beam of a certain length and material properties.

Direction: Solve each problem carefully and show your solution in each item.

#### Number of problems found: 68

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Cosine rule uses trigonometric SAS triangle calculator.