Topic--Law of Sines Investigated with GSP 4.0

The basics:

1. Law of Sines overview: Click here for introductory material related to the law of sines.

2. Law of Sines--ambiguous case: In the past, some of my biggest headaches in teaching (for both me and my students, I'm sure) have been related to the ambiguous case of the law of sines. Click on this link to see a GSP 4.0 demonstration that aids the discussion of this topic.

3. Law of Sines--proof #1: Try deriving the law of sines yourself. (Hints and suggestions are provided, as well as a complete proof if you give up.)

4. Law of Sines--proof #2: This proof of the law of sines points out a relationship between a triangle and its circumcircle.

5. Can the law of sines be used if...?

Extensions--Further proofs/problems related to the law of sines:

1. How is the area of a triangle related to the circumcircle of that triangle?

2. For any triangle ABC, b(cosC) + c(cosB) = ???

3. In any triangle ABC, a(sinB - sinC) + b(sinC - sinA) + c(sinA - sinB) = ???