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:

`a/sinA=b/sinB=c/sinC`

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

`sinB=sinA*b/a` and so `B` is known;

`C=180°-A-B` and so `C` is known;

`c=sinC/sinB*b`