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.

What values of a, b, and A make 0 triangles (ie. it is not possible to make a triangle)? Give one example when A>90degrees AND A<90.

What values of a, b, and A make 1 triangle? Give one example when A>90degrees AND A<90.

What values of a, b, and A make 2 triangles? Can this happen when A>90 degrees?

Do you have any observations?

Law of Sines - Ambiguous Case

Introduction

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.

Information: Law of Sines - Ambiguous Case