# How do you use the law of sines to solve the triangle given A = 165.1°, B = 81.9°, b = 18.6?

The law of sines says that in a triangle where the angle $\alpha$ is opposite the side of length $a$, angle $\beta$ - length $b$ and angle $\gamma$ - length $c$ and $R$ is the radius of the circumscribed circle (the smallest circle possible that contains the triangle / passes through all three vertices) we have the following:
$\frac{a}{\sin} \alpha = \frac{b}{\sin} \beta = \frac{c}{\sin} \gamma = 2 R$
and you can use any two of these, e.g. $\frac{b}{\sin} \beta = 2 R$.
In your question values $A$ and $B$ are given in degrees so one can assume that they're the angles $\alpha$ and $\beta$ but their sum is ${247}^{\circ}$ which is a little bit too much since in all triangles the sum of all three angles is always ${180}^{\circ}$. Please check where the mistake in those values is :)