Lesson 6

Discover

There are various relationships between side lengths and angles in a triangle. In Try This 1, you will explore one of these relationships.

Try This 1

When solving for angles, there are two calculator modes that can be used: radian and degree. Before beginning any trigonometry question within the Mathematics 30-3 course, ensure that your calculator is set in degree mode.

1. Use a calculator to determine the sine of 114°. Round to two decimal places.
2. Open Sine Law 1.
   
   
    
   
   1. Make sure that “Show A and a” is checked, and that “Show B and b” and “Show C and c” are not checked. In the diagram, “A” represents an angle and “a” represents the side length across from A. Copy the equation at the top of the screen and highlight where A, a, and their values are used in the equation.
   2. Try moving some of the vertices in the triangle around. Notice that A and a in the equation change as the values in the triangle change.
3.  
   1. Leave “Show A and a” visible and turn on “Show B and b” by checking the corresponding box. Watch for where the B and b values appear on the triangle. How are B and b related?
   2. Watch the two equations as you move one of the vertices of the triangle. What relationship do you notice between the equations?
   3. Using your response from part b., what can you conclude about
4. Turn on “Show C and c” so all three boxes are checked. Move a point around again. How is related to
5. Open Sine Law 2. This is very similar to Sine Law 1, but the equations are now written in the form  instead of in the form . How are and related?
   
   
    
   

Save your responses in your course folder.