Lesson 6

Explore

In Try This 1, you explored a relationship that can be used with any triangle. This relationship is called the sine law and is often written as

can also be written as

 

Again, this represents three separate equations:

• 
• 
• 

In some situations, one version of the sine law is easier to use than the other.

Another way of writing this equation is to break it into three separate equations:

means that the length of a side divided by the sine of the opposite angle is the same for all side-angle pairs in any triangle.

Watch Sine Law Illustrator to see this pictorially.

The sine law formulas reflect how mathematicians typically label triangles: sides are named with lowercase letters and angles are named with uppercase letters. Sides and their opposite angles are named with the same letter—for example, b and B.

 

You may find it helpful to view How to Label a Triangle.

 

 

The sine law can be used to determine an unknown length in a triangle. Typically, the equations with the sines in the denominator are easiest to use when determining an unknown length. Try This 2 explores this idea.

Try This 2

1. Draw the following triangle.
   
   
    
   
   
   
   1. Label the sides of the triangle with a, b, and c using the method described in How to Label a Triangle.
   2. Determine which of the following versions of the sine law would be best to find the length of the side between A and B. Explain your choice(s).

       

   3. Use your choice from part b. to determine the length of the side between A and B.
2. Explain how you could determine the third angle of the triangle using the first two angles.

Save your responses in your course folder.