MCQ
In a triangle ABC , if a $=(\sqrt{3}+1)$, $\angle B=30^{\circ}$ and $\angle C=45^{\circ}$, then c is equal to
  • A
    4
  • 2
  • C
    1
  • D
    3

Answer

Correct option: B.
2
(B) We know that,
$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=k$
$\Rightarrow \frac{ b }{\frac{1}{2}}=\frac{ c }{\frac{1}{\sqrt{2}}} \Rightarrow c -\sqrt{2} b=0$ ...(i)
By projection rule,
$a=b \cos C+c \cos B$
$\Rightarrow \sqrt{3}+1=\frac{ b }{\sqrt{2}}+\frac{\sqrt{3}}{2} c$
$\Rightarrow 2(\sqrt{3}+1)=\sqrt{2} b+\sqrt{3} c$ ...(ii)
From (i) and (ii), we get
$2(\sqrt{3}+1)=(\sqrt{3}+1) c \Rightarrow c=2$

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