1. Module 7

1.30. Page 2

Mathematics 10-3 Module 7 Lesson 6

Module 7: Lesson 6

 

Get Started

 

In this activity you will review how the cosine ratio is used to find an unknown side or angle in a right triangle.

 

Try This

 

Work with a partner, if possible.

 

You will use the math interactive “Exploring Trig Ratios—Explore It” to review how to apply the cosine ratio to find a missing side or angle in a right triangle. Follow these tips:

  • First make sure you are in “Explore It” mode and that Reference Angle is initially set to R.

  • Select cos R under Function to explore the cosine ratio.

  • Choose one of the options under Unknown to determine the unknown side or angle in the right triangle.

  • Resize the triangle by using the Scale slider, or drag the movable vertices.

  • Continue your exploration with S selected as the Reference Angle.

TT 1. Examine the steps used to solve for your unknown. How do the steps for solving for an unknown angle differ from those used to find an unknown side?

 

Save your work in your course folder. If you still have questions, ask your teacher.

 

Now you are ready to explore problem situations involving the cosine ratio.

 

Explore

 

In this activity you will determine the angle between the diagonal of a rectangular room and one of the room’s walls.

 

Try This

 

In this activity you will need an imperial tape measure and your calculator. Work with a partner, if possible.

 

Step 1: Choose a rectangular room in your home or school in which you will use your tape measure to take measurements.

 

Step 2: Measure the length of one of the walls to the nearest inch. Then measure the diagonal distance from one corner of the wall you measured, across the room, to the opposite corner. Again, measure to the nearest inch.

 

TT 2. Use your measurements to draw and label a diagram that describes your situation.

 

 

This illustration shows a birds-eye view of a rectangular room and a diagonal line from one corner to the other.

 

TT 3. Use the cosine ratio to calculate the angle between the adjacent wall and the diagonal. Show all steps.

 

TT 4. Because your measurements were in feet and inches, what did you have to do with these measurements before you could determine the angle?

 

Share

 

You are now going to share your answers to the TT 2 to TT 4 questions. Remember that sharing work is an important part of learning. To make the most of your sharing opportunity, be sure that you complete these tasks.

  • Complete TT 2 to TT 4 to the best of your ability. Have the answers in a form that you can easily share with another student or, if directed, with your teacher.

  • Use the discussion area for your class, or another method indicated by your teacher, to post your answers and to view the work of people you are sharing with.

  • Compare your answers. Identify where you have similar answers and where your answers are different. Discuss all differences between your answers until you have an agreement. If necessary, you may wish to involve your teacher in your discussion.

  • Revise your answers where necessary.

Save the revised copy of your work, including your diagram and measurements, in your course folder. Consult your teacher about whether you are to save a transcript of your discussion in your course folder as well..