So you have triangle ABC.

According to the Law of Sines, a/sin(A) = b/sin(B) = c/sin(C). Ever wonder whether these 3 ratios actually *mean* anything? It turns out that these ratios are related to the size of the circle that circumscribes triangle ABC. Help your students discover this exciting fact using the materials linked below! Don’t be that teacher that starts the lesson by writing the Law of Sines on the board, then proceeds directly to applications. Let your students *discover* this fundamental law of trigonometry, and when they are through they will write it down themselves unassisted!

Visit my Law of Sines folder on dropbox.

• Begin by viewing the Sketchpad file.  Click the button that says “Amaze Me!” and then let it run for about 30 seconds. This animation is meant to pique students’ curiosity. It suggests a proof of the Law of Sines.
• Next check out the 6-page packet labeled “Exploring the Law of Sines.”  By the time students complete this activity, they will have developed a proof of the Law of Sines!
• Formulas for Oblique Triangles is a place to record the generalizations that follow the previous activity (plus the Law of Cosines, coming up later!).
• Law of Sines #1 provides opportunities to solve triangles using the Law of Sines.  For me, this is guided notes + classwork.
• Law of Sines #2 is additional practice.  For my class: homework.

Here are the opportunities that students have to make connections to prior knowledge through this activity:

• Knowing that a triangle can be circumscribed by a unique circle
• Applying the inscribed angle theorem
• to angles inscribed in semicircles
• to oblique angles
• Applying their knowledge of basic trig functions for right triangles (sine, cosine, and tangent)

Check out the materials linked above, try them with your students, and let me know how it goes in the comments!  If you have ideas about how to improve the materials, please feel free to share those as well.