Math 20-1

Chapter 2 Trigonometry

Lesson 2.4  The Cosine Law

Support Documents

Answer pages

You should be checking your work for EVERY question you do!

To make that easy, you can download the solutions files which have the answers for all the practice problems in the text.

You can print it, though it would be a lot of pages.

I think the best choice would be to keep the files handy, and have them open and ready every time you are working on math.

This saves you the time of flipping to the back of the book every time you need to check an answer.

FOLDER LINK

Formula Page

Math 20-1 is an academic course and you will be expected to memorize a lot of what you are covering in class.

Your teacher will have expectations for the things you will see on a formula page.

The link below is to formula page that you can download and print to use with your course.

You may or may not be allowed to use this on tests, and you may or may not be allowed to ADD your own notes to these pages.

Use of this page depends on your teacher.

What goes on this page is also subjective, so it is subject to change!

Formula Page

Focus on...

Lesson Objectives

•	sketching a diagram and solving a problem using the cosine law

•	recognizing when to use the cosine law to solve a given problem

•	explaining the steps in the given proof of the cosine law

Focus on...  Activity

The FOCUS section introduces the main concept that will be covered in the lesson.

There isn’t a Focus section for this lesson.

TEXT Page 114

Read/Work through the  Focus  section at the top of page 114 in  your textbook.

Investigate  the Cosine Law

The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 114 - 115

This is a good investigation, but I’ll be using a slightly difference approach for the videos.
If your teacher asks you to do the investigation,  I am sure they will support the process.
If you wish to follow along with my videos,  see the steps below.
(I’m using a different approach so you can work on the same triangles that I am using)

Investigation (modified approach)

1.	In order to follow along, first download and print the document you can link to below.

Triangles LINK

2.	Using a protractor and ruler, measure the sides and angles in all the triangles.

3.	Classify each triangle as right, acute, or obtuse.  (using the angles)

Questions 1 - 3  Video Tutorial   INV A

4.	For each triangle,  determine the square of each of the side lengths.

5.	For each triangle,  add the squares of the lengths of the two shorter sides.
	How does this compare to the square of the length of the longer side?

Questions 4 - 5 Video Tutorial   INV B

Geogebra Applet  (I worked with this in the video) LINK

6.	In each triangle, let  a  and b  represent the lengths of the two shorter sides. and c   represent the length of the longer side.
	Calculate the value  of 2 a b cos C   for each triangle.

7.	**Can you see a way to combine the quantities you calculated in Question 5 and Question 6 into an equation that is true for all three triangles?

Questions 6 - 7 Video Tutorial   INV C

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Page 116

Read/Work through the  Link the Ideas  section on Page 116 in your textbook.

Watch

Video Tutorial  (patterns)    LINK A

Video Tutorial  (proof of the cosine law)   LINK B

Examples

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

Example 1  Determine a Distance

TEXT Pages 116 - 117

Work through Example 1 on Pages 116 - 117 in your textbook.

Watch

Video Tutorial

Your Turn

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

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  Determine an Angle

TEXT Pages 117 - 118

Work through Example 2 on Pages 117 - 118 in your textbook.

Watch

Video Tutorial

Your Turn

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

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 3  Solve a Triangle

TEXT Pages 118 - 119

Work through Example 3 on Pages 118 - 119 in your textbook.

Watch

Video Tutorial

Your Turn

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

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

Key Ideas

Key Ideas 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!

Check Your Understanding    (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!

NOTE!
There are MANY practice questions.
In the interests of time,  I will be selectively skipping some of them.
(any question that was a “one step” solution with a diagram provided,  I skipped.
You have access to the solutions, and you can use those for help as needed.
If the presentation seems straight-forward, I won’t create a video.
I’m hoping that as this course continues to be developed, that if MORE HELP is needed for a specific question,  the missing videos can be added at a later date.

Types of Practice Problems

Practice 
These questions allow you to check your understanding of the concepts. 
You can often do the first few questions by checking the Link the Ideas notes or by following one of the worked Examples.

Apply 
These questions ask you to apply what you have learned to solve problems. 
You can choose your own methods of solving a variety of problem types.

Extend 
These questions may be more challenging. 
Many connect to other concepts or lessons. 
They also allow you to choose your own methods of solving a variety of problem types.

Create Connections
These questions focus your thinking on the Key Ideas and also encourage communication. 
Many of these questions also connect to other subject areas or other topics within mathematics.

Mini Lab
These questions provide hands-on activities that encourage you to further explore the concept you are learning.

Notes

Question 1,    I didn’t do a video for this one.

Question 4,    I didn’t do a video for this one.

Question 5,    I didn’t do a video for this one.

Question 6,    I didn’t do a video for this one.
I think there is an error in the textbook here,  with the given angles , it’s possible to find EXACT answers.
Challenge yourself to do that!
The solutions provide lots of help with the process.

Question 7,    I didn’t do a video for this one.

Question 8,    I didn’t do a video for this one.

Question 9,    I didn’t do a video for this one.

Question 10,    I didn’t do a video for this one.

Question 11,    I didn’t do a video for this one.

Question 12,    I didn’t do a video for this one.

Question 13,    I didn’t do a video for this one.
Great question, but massive...   huge, multi-step problem.
If you need to do this,  the solutions provide a detailed, step by step method.

Question 15,    I didn’t do a video for this one.

Question 18,    I didn’t do a video for this one.

Question 19,    I didn’t do a video for this one.

Question 25,    A clock to help you visualize...

Question 28,    I didn’t do a video for this one.
An excellent question, but definitely an EXTEND problem!
The provided solution has lots of detail if you need help with this one.

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 2", "Question 3",  ,  }, { ,  ,  , "Question 14",  }, {"Question 16", "Question 17",  ,  , "Question 20"}, {"Question 21", "Question 22", "Question 23", "Question 24", "Question 25"}, {"Question 26", "Question 27",  , "Question 29", }})

({{"CC 30"}})

Question CC 31,    I didn’t do a video for this one.

Question CC 32,    I didn’t do a video for this one.

Question CC 33,    I didn’t do a video for this one.
A   GREAT question , but “huge”
More of a project  kind of endeavour!
Check the solutions for detailed (multi-page!) help on this one.