1. The Sine Law (animated)

2. Sine Law Let’s begin with the triangle  ABC:

3. Sine Law Let’s begin with the triangle  ABC: A C B

4. Sine Law A C B c a b Let’s begin with the triangle  ABC:

5. Sine Law A C B c a b Let’s begin with the triangle  ABC: D altitude, h h

6. Sine Law A C B c a b Let’s begin with the triangle  ABC: D Note this ratio in triangle  ABD: h

7. Sine Law A C B c a b D Note this ratio in triangle  ABD: Note this ratio in triangle  ABC: h

8. Sine Law A C B c a b D Note this ratio in triangle  ABD: Note this ratio in triangle  ABD: h

9. Sine Law A C B c a b D h

10. Sine Law A C B c a b D Therefore, we get: h

11. Sine Law A C B c a b Therefore, we get: and, if we follow the same method for sides A and C: In conclusion: The Sine Law: