Question

In $△ABC$, if $a=\sqrt{3}+1,B={30}^o$ and $C={45}^o$, then $c$ is equal to

• A. $2$
• B. $3$
• C. $4$
• D. None of these

Answer 1

Answer: (A)

$2$

Using sine rule, $\frac{a}{\sin A}=\frac{c}{\sin C}$

We have, $A=180-75={105}^{\circ }$

$\therefore c=\frac{\sqrt{3}+1}{\sin {105}^{\circ }}\sin {45}^{\circ }=\frac{\sqrt{3}+1}{\sqrt{3}+1}2\sqrt{2}\frac{1}{\sqrt{2}}=2$