Lesson 5

Lesson 5: The Cosine Law

 

Focus

 

© shiyana/30449451/Fotolia

 

David and Jennifer are designing an obstacle course. They have a number of different tasks that participants need to complete along the course. David and Jennifer need to determine what supplies to purchase in order to construct the course. They are able to directly measure angles and distances for many of the tasks, but some of the angles and distances aren’t easily measured directly.

 

For the first task, participants will hang onto a rope while crossing a rapidly flowing stream that is about 1 m deep. David and Jennifer need to know the distance across the stream to be sure that the rope is long enough.

 

They don’t have a tape measure long enough to measure this distance, so they decide to calculate this value by creating a triangle using measurements they can make. If you can create a triangle using values that can be measured, you can often calculate the missing value using trigonometry.

 

 

David and Jennifer know the measures of the canyon walls and the angle at the bottom, as shown in the following diagram. The rope corresponds to

 

You will discover as you work through the lesson how David and Jennifer can determine the value of

 

Outcomes

 

At the end of this lesson you will be able to

• use the cosine law to solve for sides or angles in oblique triangles

Lesson Questions

 

You will investigate the following questions:

• How can angles and sides in any triangle—oblique and right—be found?
  
  
• How do you determine when to use the sine law and when to use the cosine law?

Assessment

 

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 5 Assignment (Download the Lesson 5 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 2 Glossary Terms and Formula Sheet
  
  
• work under Project Connection