1. The Sine Law (animated)

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

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

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

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

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

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

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

9. A CB c a b Sine Law h D

10. A CB c a b h D Therefore, we get:

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