Lesson 7

Discover

 

In the next activity you will explore how Jennifer and David’s problem from Focus can be solved.

 

Try This 1

1.  
   1. Sketch a triangle to represent the problem from Focus.
   2. Explain why the Pythagorean theorem cannot be used to solve this problem.
   3. Write out all three equations of the sine law using values from the triangle you drew in part a.
   4. Explain why the diagram does not include enough information for you to use the sine law to determine length a.
      
      Since the sine law cannot be used, you will have to explore a different relationship. One possibility is the cosine law. Open the Cosine Law Explorer.
      
      
       
      
      
2.  
   1. The Cosine Law Explorer shows a cosine law equation and how it can be filled in using the values from the triangle. Explain where each value on the triangle is substituted into the original equation.
   2. Watch the last equation as you move a point around. What do you notice?
   3. Using your response from part b., what relationship can you predict between a2 and b2 + c2 − 2bc cos A? Do you expect this relationship will hold for all triangles?
3. Use the equation a2 = b2 + c2 − 2bc cos A to solve Jennifer and David’s problem. The following steps may be useful.
   • Determine which value on the triangle corresponds to each variable in the equation.
   • Substitute the known values into the equation.
   • Simplify the equation where possible
   • Once you know what a2 is equal to, you can take the square root of both sides to determine the value of a.

Save your responses in your course folder.

 

Share 1

 

Share your responses with a classmate. In your sharing session, be sure to address the following points.

1. How can you decide if there is enough information in a triangle to use the cosine law?
2. How can you decide if there is enough information in a triangle to use the sine law?

If required, place a summary of your discussion in your course folder.