Copy of Law of Sines - Ambiguous Case
Introduction
If the given information in a Law of Sines problem is a SSA triangle, there are either 0, 1, or 2 triangles that are satisfy those conditions. That is why this type of triangle is called the Ambiguous Case. In this activity, you will explore the factors that impact the number of possible triangles.
Find different combinations of a, b, and A that results in different numbers of triangles. Move the point C to change angle A and use the sliders to change the lengths of a and b.
Answer the following questions for A < 90 degrees
What values of a, b, and A make 0 triangles (ie. it is not possible to make a triangle)?
What values of a, b, and A make 1 triangle?
What values of a, b, and A make 2 triangles?
Do you have any observations?
Answer the following questions for A > 90 degrees
What values of a, b, and A make 0 triangles (ie. it is not possible to make a triangle)?
What values of a, b, and A make 1 triangle?
What values of a, b, and A make 2 triangles?
Do you have any observations?