Question

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

Answer 1

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;

$C={180}^o-A-B$ and so C is known;

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