Math 20-2

Chapter 3 Acute Triangle Trigonometry

Lesson 3.1 Exploring Side–Angle Relationships in Acute Triangles

GOAL

The goal of this lesson is stated at the top of page 130 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Explore the relationship between each side in an acute triangle and the sine of its opposite angle.

Formula Pages  (Unit 3)

This will be up to your teacher, but I have created a set of formula pages you can use for this unit.
It contains all the Key Ideas from the lessons in Unit 3.
You can download and print this file to use for your work in this math class.

LINK
https://drive.google.com/file/d/1oy-OS5msv8UPIwn90LBbmRkScgZLaDZc/view?usp=sharing

Explore the Math

A chance to explore the ideas of the lesson

TEXT Page 130

Read/Work through the Explore the Math section on Page 130 in your textbook.

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

NOTE!   There is a small error in the textbook diagram  (page 130)
The angle shown as 50.4° should actually be 50.2°   
(not that it makes much difference to the calculations!  but it does mean the angles add to 180°, as they should...)

Demonstration

A simple demonstration that shows that any triangle can be broken down into right triangles.
We will use this to prove the sine law and the cosine law.

Introduction

Video Tutorial  (Explore 1)

?  What are two equivalent expressions that represent the height of Δ ABC ?

This is a huge thing the textbook is asking you to do (with no help)
You need to use what you (hopefully) remember about your RIGHT TRIANGLE TRIGONOMETRY to represent the height of the triangle in different ways.
Then, use those expressions to create a special equation.
If you can do this on your own,  WOW!!   really... WOW!

If you need some help , use the video below
(and remember, as always, you can PAUSE the video anytime and do some math yourself!  use the video to help YOU do the exploration as much as possible)

Video Tutorial   (Explore 2)
Working with the triangle on the left

Video Tutorial   (Explore 3)
Working with the triangle on the right

Reflecting

Part A  if you have a classmate,  great,  you can answer this question.
If not,  head to part B

Part B1  Video Tutorial  for the triangle on the left
Part B2  Video Tutorial  for the triangle on the right

Part C  I included this step in the previous videos.

Part D  Video Tutorial

Interactive Applet

THIS Geogebra Applet Illustrates the ideas of this lesson perfectly.

Video Tutorial

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!

Further Your Understanding

Further Your Understanding problems reinforce the math presented in this lesson.

These are just practice problems with a different heading....

•	Work through these 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!

Notes

Question 5,    I didn’t do a video for this one.
A great question, and if you do it,  WELL DONE!
However,  the Geogebra Applet with the link in the lesson does a great job of illustrating this, for MULTIPLE triangles, instead of just one example.
(you can drag the triangle in the applet so you get (close) to a right triangle, check the ratios, then drag the triangle into a different shape with a 90° angle)
THIS Geogebra Applet Illustrates the ideas of this lesson (and Question 5) perfectly.

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"}})