If the angles of a $∆$ABC are 30°, 45° and the included side is $\sqrt{3}+1$, then the remaining sides are

Let $\mathrm{\angle }\mathrm{B}={30}^{\circ }\mathrm{\angle }\mathrm{C}={45}^{\circ }\Rightarrow \mathrm{\angle }\mathrm{A}={105}^{\circ }\Rightarrow$
$$\begin{gathered} \frac{\sqrt{3}+1}{\sin {105}^{\circ }}=\frac{\mathrm{b}}{\sin {30}^{\circ }}\Rightarrow \mathrm{b}=\frac{(\sqrt{3}+1)\sin {30}^{\circ }}{\sin {105}^{\circ }}=\frac{(\sqrt{3}+1){\displaystyle \frac{1}{2}}}{{\displaystyle \frac{(\sqrt{3}+1)}{2\sqrt{2}}}}=\sqrt{2} \\ \text{and }\frac{\mathrm{c}}{\sin {45}^{\circ }}=\frac{\sqrt{2}}{\sin {30}^{\circ }}\Rightarrow \mathrm{c}=\frac{\sqrt{2}\left(\sin {45}^{\circ }\right)}{\sin {30}^{\circ }}=2 \end{gathered}$$