In these worksheets, students will use the Law of Sines and the Ambiguous Case.

#### The Law of Sines is an equation that describes the relationship between the lengths of the sides of any shape (in this case triangles) to the sines of its angles. When the Law of Sines is used to determine the missing measurement values of a triangle when given two sides and an angle opposite one of those sides (SSA), it is called the Ambiguous Case. This law is the connector between the oblique angles and the sides of a triangle. To put it differently, it simply is the ratio of one of the side’s length and the sine of the opposite angle. In retrospect, for a triangle ABC which is oblique with the sides a, b, and c, the law of sines will be: a / sin⁡A = b / sin⁡B = c / sin⁡C. To use the Law of Sines, you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an angle opposite one of them (SSA).

There are 12 worksheets in this set, divided into two sets of 6. In the first set, students will use the Law of Sines to solve problems. In the second set, students will use the Law of Sines and the Ambiguous Case. These are moderately complex problems and a sound understanding of trigonometry is required in order for students to be successful with these worksheets. 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 use the Law of Sines and the Ambiguous Case. These worksheets explain how to use the Law of Sines and the Ambiguous Case. Sample problems are solved and practice problems are provided.

# Law of Sines Worksheets

## Law of Sines Lesson

Students will learn how to approach this type of exercise: In Δ TRP, side t = 24, m ∠ T = 45° and m ∠ P = 55°. Find side p to the nearest tenth of an integer.

## Worksheet

Students will use the Law of Sines to solve triangle related problems. Ten problems are provided.

## Practice

You will apply this skill to solve for missing angles and sides within triangles.

## Review and Practice

The concept of how to use the Law of Sines to solve problems is reviewed. A sample problem is solved. Six practice problems are provided.

## Quiz

Students will demonstrate their proficiency in using these concepts to solve many unique types of questions. Ten problems are provided.

## Check

This is a great way for teachers to explore this skill with their entire classes at the same time.

## Lesson

This worksheet explains the following step by step: In Δ ABC, a = 18, c = 9, and m <A = 60°. How many distinct triangles can be drawn given these measurements?

## Worksheet

Students will use and apply all their knowledge of the Law of Sines and the Ambiguous Case to attempt the ten problems that are provided.

## Practice

You will find all types of missing angles and lengths of triangle sides.

## Review and Practice

This is one of my favorite topics. We work on this: How many distinct triangles can be drawn given these measurements?

## Quiz

Students will demonstrate their proficiency with using the Law of Sines and the Ambiguous Case. Ten problems are provided.

## Check

See where you stand with this concept by completing the different problems that have stuck out.