This section on Trigonometry 2 – Apprenticeship and Workplace Mathematics 10 is made up of several lessons. Lessons, Essential Questions, Focus, Get Started, Activities, Explore, Bringing Ideas Together and Lesson Summary.

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The content in this book relates to material at a Grade 10 level, and very useful for students considering exiting the school system in year 10 for an apprenticeship, internships, or trade, or adults returning to gain a qualification.

**Table of Contents**

Section Organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Trigonometry II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Lesson A: The Cosine Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Lesson B: Using the Cosines to Solve Problems. . . . . . . . . . . . . . . . . 33

Lesson C: General Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79

Data Pages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81

Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107

**Sample from Trigonometry 2 – Apprenticeship and Workplace Mathematics 10**

Imagine the excitement of carrying the Olympic torch! More than 12 000 torchbearers from all parts of Canada carried the flame during the 106-day relay that started in Victoria, British Columbia. The torch route went through all of the territories and provinces of Canada, and ended in Vancouver, the host city of the 2010 Winter Olympic Games.

Wayne Gretzky had the honour of lighting the outdoor cauldron—what a spectacular event! Take a close look at that cauldron. Its design incorporates many of angles and triangles! The Winter Olympics required many new facilities, and these buildings and structures were designed by architects who applied mathematics.

One of their mathematical tools is trigonometry.

In this section you will:

• apply similarity to right triangles.

• generalize patterns from similar right triangles.

• apply the trigonometric ratios tangent, sine, and cosine to solve problems.

<end of sample page>

### Lessons

Lessons have a combination of reading and hands-on activities to give you a chance to process the material while being an active learner. Each lesson is made up of the following parts:

**Essential Questions**

The essential questions included here are based on the main concepts in each lesson. These help you focus on what you will learn in the lesson.

**Focus**

This is a brief introduction to the lesson.

**Get Started**

This is a quick refresher of the key information and skills you will need to be successful in the lesson.

**Activities**

Throughout the lesson you will see three types of activities:

• Try This: activities are hands-on, exploratory activities.

• Self-Check: activities provide practice with the skills and concepts recently taught.

• Mastering Concepts: activities extend and apply the skills you learned in the lesson.

You will mark these activities using the solutions at the end of each section.

**Explore**

Here you will explore new concepts, make predictions, and discover patterns.

**Bringing Ideas Together**

This is the main teaching part of the lesson. Here, you will build on the ideas from the Get Started and the Explore. You will expand your knowledge and practice your new skills.

**Lesson Summary**

This is a brief summary of the lesson content as well as some instructions on

what to do next.

At the end of each section you will find:

**Solutions**

This contains all of the solutions to the Activities.

**Appendix**

Here you will find the Data Pages along with other extra resources that you need to complete the section. You will be directed to these as needed.

**Glossary**

This is a list of key terms and their definitions.

Throughout the section, you will see the following features:

**Icons**

Throughout the section you will see a few icons used on the left-hand side of

the page. These icons are used to signal a change in activity or to bring your

attention to important instructions.

**Materials and Resources**

There is no textbook required for this course.

You will be expected to have certain tools and materials at your disposal while working on the lessons. When you begin a lesson, have a look at the list of items you will need. You can find this list on the first page of the lesson, right under the lesson title. In general, you should have the following things handy while you work on your lessons:

• a scientific calculator

• a ruler

• a geometry set

• Data Pages (found in the Appendix)

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