Solving a system of question involving sine

Question

I have this formula

$$ \frac{\sin \left(30^{\circ} - \text{Angle }A\right)} {\sin \left( \text{Angle }A\right)} = \frac{\text{Side }B} {\text{Side }A} $$

How do I solve for AngleA?

Answer 1

You can write $$\frac{\sin(30^{\circ})\cos(\alpha)-\cos(30^{\circ})\sin(\alpha)}{\sin(\alpha)}=\sin(30^{\circ})\cot(\alpha)-\cos(30^{\circ})=\frac{b}{a}$$