Math 10C

Chapter 3 Right Triangle Trigonometry

Lesson 31 The Tangent Ratio

Focus

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

TEXT Page 100

Read/Work through the  Focus  section on page 100 in  your textbook.

Investigate

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

TEXT Pages 101 - 102

Read/Work through the  Investigate  section on Page2 101-102 in your textbook.

If you are interested, here is a short video that gives you a bit of background on the idea of tacking   (sailing in the direction of the wind by going back and forth, slightly off course each time)

YouTube Link

This will be easiest to do if you use 1 cm grid paper,  that you can download and print using the link below.

The folder you can  link to below has grid paper files you can download/print

LINK

Watch

TONS of videos here, but basically, this is all the teaching for the entire trigonometry unit.

Video Tutorial Introduction

Video Tutorial   Similarity

Video Tutorial   Similar Triangles

Video Tutorial   Measure

Video Tutorial   Calculate

Video Tutorial   Degrees Mode

Video Tutorial   The tangent ratio

Video Tutorial   Misc. information about right triangles

Right triangles

A simple demonstration showing that ANY triangle that is NOT a right triangle CAN ALWAYS be divided into two right triangles in multiple ways.
This is why working with RIGHT TRIANGLES is so useful, it reduces the number of possible scenarios, but still produces results that are helpful for ANY triangle.

Link the Ideas

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

TEXT Page 103

Read/Work through the  Link the Ideas  section on Page 103 in your textbook.

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  Write a Tangent Ratio

TEXT Page 103

Work through Example 1 on Page 103 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  Calculate a Tangent and an Angle

TEXT Page 104

Work through Example 2 on Page 104  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  Determine a Distance Using the Tangent Ratio

TEXT Page 105

Work through Example 3 on Page 105 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 4  Determine an Angle Using the Tangent Ratio

TEXT Page 106

Work through Example 4 on Page 106 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!

Types of Practice Problems

Practice questions require basic understanding of the ideas of the  lesson.

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

Extend questions offer enrichment and extension.

Create Connections questions connect the math to everyday contexts.

Mini Lab (optional)  your teacher may or may not have you do these.

Notes

Question 18,    a graphic organizer. Great question, but I didn’t make a video.  I could talk for seconds, minutes, hours....   if I really answered this it would be like teaching the whole lesson again....

Question 21,    another GREAT question if you actually go to the trouble to make the transit.  Lots of videos showing the process.  Here is one that I think was done by a student.  LINK

This would be a good project,  and a good thing to make a more detailed video for,  I might add this at a later date if your teacher or enough students request it.

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 14", "Question 15"}, {"Question 16", "Question 17",  , "Question 19", "Question 20"}})