Grade 9 Integrated Math Lesson Notes Outline

Lesson 1: Trigonometry Exploration Unit 3 – Trigonometry

(A)Lesson Context

 How do I determine the measure of angles in geometric shapes, without direct BIG PICTURE of this UNIT: measurement?  How do I solve for sides or angles in right triangles?  How do I model real world scenarios using right triangles? Where we’ve been Where we are Where we are heading CONTEXT of this LESSON: You know how to work What is the relationship between How can I solve problems with sides and angles of the ratios of sides of right triangles that require geometric right triangles. and the measure of the non-right models using right angles in the right triangle triangles?

(B)Lesson Objectives:

a. Exploring the relationship between the ratio of the sides of a right triangle and the measurement of the non-right angles

b. Introduce terminology used in trigonometry Lesson 1: Trigonometry Exploration Unit 3 – Trigonometry

Exploring Ratios

Exercise 1: Please follow the link on the IM2 Website Unit 3. You will be working with Triangles of different sizes but that have the same angles. Your job will be to make triangles with the given angles, record the needed informaiton in the table below, and make some observations.

Adjacent Opposite Hypotenuse opposite opposite adjacent Side Side adjacent hypotenuse hypotenuse 0 Adjacent Opposite Hypotenuse opposite opposite adjacent qq12==10 Side Side adjacent hypotenuse hypotenuse

Adjacent Opposite Hypotenuse opposite opposite adjacent q3 = Side Side adjacent hypotenuse hypotenuse

Exercise 2: Pick two of the angles you measured and write some observations you made about the ratios given.

q = Describe the pattern for the different ratios when you change the side length of the adjacent side. opposite adjacent opposite hypotenuse

adjacent hypotenuse

q = Describe the pattern for the different ratios when you change the side length of the adjacent side. opposite adjacent opposite hypotenuse

adjacent hypotenuse

Exercise 3. Mr. Smith and Mr. Santowski (Mr. Rawlings was busy grading your tests) have measured some triangles with angles between 1o and 89o and put them into the table below.

Angle  Opp/Hyp Adj/Hyp Opp/Adj Angle  Opp/Hyp Adj/Hyp Opp/Adj

 = 7o .1219 .9925 .1228  = 48 o .7431 .6691 1.1101

 = 12 o .2079 .9781 .2126  = 50 o .7660 .6428 1.1918

 = 15 o .2588 .9695 .2679  = 52 o .7880 .6157 1.2799

 = 21 o .3584 .9336 .3839  = 68 o .9272 .3746 2.4751

 = 43 o .6820 .7313 .9325  = 89 o .9998 .0176 57.29

 = 45 o .7071 .7071 1.0000

See if you can use this table to help you find the missing lengths in the triangles given. Please explain your reasoning and show your work.

 =  =  = Side Given: Side Given: Side Given: Looking For: Looking For: Looking For: Lesson 1: Trigonometry Exploration Unit 3 – Trigonometry

The Big Idea: Now, all these ratios don’t require the arduous measuring work that we had to do to get them. They actually have all of them in your calculator already. They are called sine, cosine, and tangent. Please fill out the following table using your sin(), cos(), and tan() on your calculator. Make sure your calculator is in degree MODE. Observe which function goes with which ratio. Use the angle measuremets you used in Exercise 1.

Angle  sin() cos() tan()  = 10  =  =  =

The Big Idea: This is the main idea of Right Triangle Trigonometry

sin() =

cos() =

tan() =

Closure: Can you use your understanding of the side length ratios and sine, cosine, and tangent funcitons on your calculator to find the missing sides in the triangles below? Lesson 1: Trigonometry Exploration Unit 3 – Trigonometry

2o 1563 mi 956.75 ft

 =  = Side Given: Side Given: Looking For: Looking For:

189 ft

.075 cm

 =  = Side Given: Side Given: Looking For: Looking For:

Extension Activity:

Angle  Opp/Hyp Adj/Hyp Opp/Adj Angle  Opp/Hyp Adj/Hyp Opp/Adj Lesson 1: Trigonometry Exploration Unit 3 – Trigonometry