# What is the Law of Sines?

Jan 30, 2015

First of all it is useful to say the notation in a triangle:

Opposite at the side $a$ the angle is called $A$,
Opposite at the side $b$ the angle is called $B$,
Opposite at the side $c$ the angle is called $C$.

So, the Sinus Law can be written:

$\frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{\sin} C$.

This Law is useful in all the cases SSA and NOT in the case SAS, in which the Law of Cosinus has to be used.

E.G.: we know $a , b , A$, then:

$\sin B = \sin A \cdot \frac{b}{a}$ and so $B$ is known;

C=180°-A-B and so $C$ is known;

$c = \sin \frac{C}{\sin} B \cdot b$