1. Lesson 4

1.5. Explore 4

Mathematics 20-1 Module 2

Module 2: Trigonometry

 

The Sine Law Ambiguous Case

 

The ambiguous case is the name mathematicians use for scenarios like Example 2: Mars Exploration Rover. The ambiguous case occurs whenever you are trying to solve a triangle problem and the only given information is two sides and an angle opposite one of those sides. Whether or not a triangle falls under the ambiguous case depends on the measures of the sides and angle given.

 

Try This 3

 

This is a play button that opens Ambiguous Case Explorer.

c GeoGebra Creative Commons Attribution-Share Alike 3.0 or later

You will use Ambiguous Case Explorer to investigate the different possibilities in a similar scenario.



In this scenario the given information is as follows:

  • ∠A = 36°

  • = 3.8

  • = a value that you specify

By changing the length of using the slider at the bottom, you also change the number of triangles that can be created with the specified sides and angles.

 

Answer the following questions using Ambiguous Case Explorer.

  1. What are the conditions for the length of that result in no possible triangles?

  2. What are the conditions for the length of that result in one possible triangle?

  3. What are the conditions for the length of that result in two possible triangles?

  4. Are there values for the length of that result in more than two possible triangles?

  5. Based on your observations, create a rule that relates the length of to the number of possible triangles.
Share 3

 

Share your observations in question 5 of Try This 3 with a partner. Try to come to agreement on the rule.