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 Graphing Calc Interactive Scientific Calc

# The Law of Cosines

## Formula and examples of law of cosines

### Law of Cosines Formula

The law of cosines is a formula that relates the three sides of a triangle to the cosine of a given angle. This formula allows you
Video Tutorial of Law on Law of Cosines
Interactive Demonstration of the Law of Cosines Formula
The interactive demonstration below illustrates the Law of cosines formula in action. Drag around the points in the triangle to observe who the formula works.
The two common problems types that are suitable for the law of cosines are.
Problem type 1: when you know the lengths of 2 sides of a triangle and the angle in between the two sides
Problem type 2: when you know the lengths of three sides of a triangle and want to know a particular angle

#### Example of Law of Cosines Formula

• x² = 10² + 14² −2(10)(14)cos(44°)
• x² = 296 −280cos(44)
• x² = 94.6

## Law of Cosines to Find a Side Length

Practice Problem 1) Use the law of cosines formula to calculate the length of side A.
Practice Problem 2) Use the law of cosines formula to calculate the length of side A.

 Step 1: set up the formula
Practice Problem 3)Use the law of cosines to calculate the length of side x.

## Law of Cosines to Find an Angle

Practice Problem 3) Use the law of cosines to calculate x.
 Step 1: set up formula
Practice Problem 4) Use the law of cosines to calculate the measure of the shaded angle.
 Step 1: set up formula
The law of Cosines and the Pythagorean theorem.

Use the law of cosines to calculate the value of x. This exercise should help you see the connection between the law of cosines and the Pythagorean theorem.
 Explanation