1. Lesson 1

1.4. Discover

Mathematics 20-2 M1 Lesson 1

Module 1: Trigonometry

 
Discover
 

In previous math courses, the emphasis in trigonometry was single triangle problems. In Mathematics 20-2 you will be solving a variety of problems involving more than one triangle. In this section you will examine problems that involve more than one triangle and the strategies for solving for sides and angles.

 

Share 1

 

course folder

After a discussion with your teacher, you will decide how to connect with other students for Share activities. Follow your teacher’s instructions to complete this Share activity. Place a summary of your Share discussion in your course folder. For more information on Share discussions, refer to the Course Introduction.

 

Eamon was asked to determine the length of side w in the following diagram.

 

 

This is a picture of two right triangles that share a side labelled y. The first triangle has a hypotenuse with length 4 units. One side is labelled y, and the final side has a length of 2.6 units. The second triangle has a hypotenuse labelled w, one side has a length of 3 units, and the final side is labelled y.

 

Eamon used the following steps to determine the length of side w:

 

Step 1: y2 + 2.62 = 42

 

Step 2: y2 + 6.76 = 16

 

Step 3: y2 = 16 − 6.76

 

Step 4: y2 = 9.24

 

Step 5:

 

Step 6: y = 3.0397...

 

Step 7: y = 3.0

Step 8: 32 + y2 = w2

 

Step 9: 9 + 9.24 = w2

 

Step 10: 18.24 = w2

 

Step 11:

 

Step 12: w = 4.2708...

 

Step 13: w = 4.3

 

 

 

With a partner, discuss and come to agreement on the following questions.

  1. The set of steps have been split into two groups. Describe what Eamon was doing in the left column, and describe what he was doing in the right column.

  2. Why did Eamon perform the steps in the left column?
Share 2
 

Nasreen was asked to determine the length of side p in the following diagram.

 

 

This is a picture of two right triangles that share an unlabelled side. The first triangle has a 43 degree angle. The hypotenuse has a length of 4.7 units, the side adjacent to the 43 degree angle is unlabelled, and the side opposite to the 43 degree angle (unlabelled) is shared with the second triangle. The second triangle has a hypotenuse with length 3.7 units. The side not shared with the first triangle is labelled p.

 

Nasreen used the following steps to determine the length of side p:

 

Step 1:

 

Step 2:

 

Step 3: 4.7(sin 43°) = y

 

Step 4: y = 2.6282...

 

Step 5: y = 2.6

 

Step 6: p2 + y2 = 3.72

Step 7: p2 + (2.6282...)2 = 3.72

 

Step 8: p2 − 13.69 − (2.6282...)2

 

Step 9: p2 = 10.4846...

 

Step 10:

 

Step 11: p = 3.2379...

 

Step 12: p = 3.2

 

 


Notice that Nasreen did not round her answers until she got to the final answer of the problem.

 

With a partner, discuss and come to agreement on the following questions.

  1. The set of steps have been split into two groups. Describe what Nasreen was doing in the left column, and describe what she was doing in the right column.

  2. Why did Nasreen perform the steps in the left column?

  3. Nasreen and Eamon both chose to group their solutions into two sets of steps. What is similar about their groupings?