Math 20-2

Chapter 3 Acute Triangle Trigonometry

Lesson 3.3  Proving and Applying the Cosine Law

GOAL

The goal of this lesson is stated at the top of page 144 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Explain the steps used to prove the cosine law. Use the cosine law to solve triangles.

Explore...

Try to answer the question in the sidebar on page 144.

As a challenge,  try to use all of the following methods at least once when you do the question
(there are multiple methods you could use to do this question)
•	right triangle trigonometry
•	the Pythagorean Theorem
•	the sine law

Hints

The question is pretty open ended.
If you want a few hints to take you through this step by step,  follow the steps below.

Hint 1

You have a right triangle and you know one angle is 50°.
What is the measure of the other angle?

Answer

The sum of the angles in a triangle is 180°.
We have 90° and 50°,  so the third angle is 40°

Hint 2

If one of the sides has a length of 8 cm,  how many different triangles could be formed?

Answer

The side of 8 cm could be opposite the 40° angle, the 50° angle, or the 90° angle.
So three different triangles could be formed.

Watch

Video Tutorial

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 144 - 145

Read/Work through the Investigate section on Pages 144-145 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

Try to follow Heather’s proof.

Video Tutorial  (Introduction)

?  How can you improve Heather’s explanations in her proof of the cosine law?

Be sure to work through the investigation as best as you can, before you watch the video!!

In the video for this section, I will go through each step  (Parts A - I)  and explain the why and the how.

Video Tutorial

Apply the Math  (Examples)

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the examples as models.

Example 1  Using reasoning to determine the length of a side

TEXT Page 146

Work through Example 1 on Page 146 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Using reasoning to determine the measure of an angle

TEXT Pages 147 - 148

Work through Example 2 on Pages 147 - 148 in your textbook.

Watch

Video Tutorial

Your Turn

I didn’t do a video for this question.

Example 3  Solving a problem using the cosine law

TEXT Page 149

Work through Example 3 on Page 149 in your textbook.

Watch

Video Tutorial

Your Turn

There isn’t a Your Turn question for this example.

In Summary

Key Ideas and Need to Know 
Presents and summarizes  the main new concepts of the lesson

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 14,    I didn’t do a video for this one.

Question 17,    I didn’t do a video for this one.
I wasn’t sure if the given value,  14 cm,  represents the length of the ARC, or the length in the triangle.
roughly triangular...?  so the curved part isn’t really there..

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13",  , "Question 15"}, {"Question 16",  , , , }})