In these worksheets, students will use the Law of Cosines to solve problems.

#### Belonging to important branch mathematics is trigonometry, which helps in determining the nature of a triangle. To do that, there are different laws that can help you in the process. One of the most important laws is the Pythagoras theorem, which is also a law that helps in determining other laws; the law of cosine is one of them. This law works on all parts of the triangle. It only depends on which information of the triangle is given to you. The law of cosine is: c2 = a2 +b2 - 2ab cos C. The two other versions of the law of cosines are: a2 =c2 +b2 - 2bc cos A. And b2 =a2 +c2 -2ac cos B. Since all three versions differ in terms of labeling of the triangle, you can just verify one of them, and you are good to go. The Law of Cosines involves the relation of the lengths of the sides of a triangle to the cosine of one of its angles.

In these worksheets, students will use the law of cosines to solve problems. Problems are presented as word problems, and students will be required to write the problem as an equation and then solve. Extra paper may be required in order for students to do their calculations. Some worksheets also include a diagram of a triangle for student reference in solving the problems. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. It also includes ample worksheets for students to practice independently. Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to solve word problems using the Law of Cosines. These worksheets explain how to use the Law of cosines. Sample problems are solved and practice problems are provided.

# Laws of Cosine Worksheets

## Cosines Lesson

This worksheet explains how to find the value of x using the figure cosine of a given angle. A sample problem is solved, and two practice problems are provided.

## Worksheet

You will be given an angle and side. The goal is to find the missing length of the triangle. Ten problems for you to tackle.

## Practice

We work with the same concept and skills to determine the measure of the hypotenuse. You get ten practice exercises to work with here.

## Review and Practice

The concept of how to find the value of x using the cosine of the given angle is reviewed. A sample problem is solved. Six practice problems are provided.

## Quiz

Students will demonstrate their proficiency with this skill on a nice quiz that will give you ten problems to complete and be graded on.

## Check

This is a nice way to review this skill with all your students at one time. Three problems are provided, and space is included for students to copy the correct answer when given.

## Lesson

This worksheet explains how to approach this problem: In Δ XYZ, side y = 8, side z = 4 and m ∠ X = 60°. Find side 'x' to the nearest integer. This problem involves all three sides but only one angle of the triangle. This fits the profile for the Law of Cosines. x2 = y22

## Law of Cosines Worksheet

Students will use the Law of Cosines to solve problems like this: Three sides of a triangle measure 5m, 6m, and 10m. Find the largest angle of the triangle to the nearest degree.

## Practice

Ten problems for you to tackle that are similar to this: In Δ ABC a parallelogram, the adjacent sides measure 15 cm and 12 cm. If the larger angle of the parallelogram measure 20° , find the length of the larger diagonal, to the nearest integer.

## Review and Practice

The concept of how to use the Law of Cosines to solve problems is reviewed with problems like this: In Δ XYZ, m

## Quiz

Students will demonstrate their proficiency with using all the skills and concepts that we have explored together. Ten problems are provided.

## Skills Check

An awesome worksheet for reviewing or introducing this skill to a whole class.