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°.




	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°.