# How do you find possible triangles given two sides and an angle (SSA)?

Jan 30, 2015

The answer is: with the Sinus Law.

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:

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

So, if (e.g.) we know $a , b , A$ (SSA), then:

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

C=180°-A-B and so $C$ is known;

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