**Home**
/ **Review
Topics**

# Law of
Cosines

The Law of Cosines can be used to solve a triangle when either
(1)two sides and the included angle are known, or (2)three sides are
known. A statement of the Law of Cosines is given below:

For any triangle with sides a, b, and c and opposite angles

_{},
respectively,

_{}

Let’s look at an example that shows how to use the Law of Cosines.

Example

Given two sides of a triangle
_{} and the angle _{} find the remaining parts of the triangle.

Solution

We
can use the Law of Cosines to find the missing side c. See figure
1.

_{}

We
can use the Law of Cosines again to find the missing angles:

For
a,

_{}

For
b,

_{}

Notice
that _{}, which is what we would expect (except for rounding
error) since the sum of the measures of the angles in a triangle should
always be 180°.

##