Question

If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know},A+B+C=\mathrm{\pi } \\ \therefore A=\mathrm{\pi }-\left(\mathrm{B}+\mathrm{C}\right) \\ \Rightarrow A=180°-\left(45°+105°\right)=30° \\ \mathrm{Now}, \\ \mathrm{According}\mathrm{to}\mathrm{sine}\mathrm{rule},\frac{a}{\mathrm{sinA}}=\frac{b}{\mathrm{sinB}}. \\ \Rightarrow \frac{2}{\sin 30°}=\frac{b}{\sin 45°}\left(\because a=2,\angle B={45}^{°}\right) \\ \Rightarrow \frac{2}{{\displaystyle \frac{1}{2}}}=\frac{b}{{\displaystyle \frac{1}{\sqrt{2}}}} \\ \Rightarrow 4\times \frac{1}{\sqrt{2}}=b \\ \Rightarrow b=2\sqrt{2} \end{gathered}$$