The Law of Sines is the relationship between sides and angles in any triangle.
The sides of a triangle are to one another
in the same ratio as the sines of their opposite angles.
Consider this triangle:
Then, the Law of Sines states that:
The law can also be written as the reciprocal:
The perpendicular, oc, splits this triangle into two right-angled triangles. This lets us calculate h in two different ways
- Using the triangle cao gives
- Using the triangle cbo gives
- Eliminate h from these two equations
By using the other two perpendiculars the full law of sines can be proved. QED.