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. **
Let's see...

Consider this triangle:

Then, the Law of Sines states that:

The law can also be written as the reciprocal:

**Proof:**

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

- Rearrange

By using the other two perpendiculars the full law of sines can be proved. **QED.**

**
**Find c

= ;
c·sin50=10·sin88;
c= ;
c=13.05