Given 2 angles find the third angle for all triangles ?
The following 6 trignometric equations describe 6 facts for finding all the angles for all triangles:
$\sin B\cos C + \cos B\sin C=\sin A$
$\sin B\sin C - \cos B\cos C=\cos A$
$\sin A\cos C + \cos A\sin C=\sin B$
$\sin A\sin C - \cos A\cos C=\cos B$
$\sin A\cos B + \cos A\sin B=\sin C$
$\sin A\sin B - \cos A\cos B=\cos C$
And the ratio represents the lenghts of all triangles when the base of the triangles are equal to $1$ unit of lenght, same as hypotenuse for a right angle triangles.
$\frac{\sin A}{\sin C}=a$
$\frac{\sin B}{\sin C}=b$
$\frac{\sin C}{\sin C}=c$
You can just use that $$A+B+C=\pi\text{ (radians)} = 180 \text{ (degrees)}.$$ This identity is present in any 2D triangle (of course in euclidean geometry).