If in any , =105^ , =45^ ,a=2, then find b. - Vidyadip

Question

If in any $\triangle\text{ABC},\angle\text{C}=105^\circ,\angle\text{B}=45^{\circ},\text{a}=2,$ then find b.

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Answer

$\angle\text{C}=105^{\circ},\angle\text{B}=45^{\circ},\text{a}=2$
From here we can calculate that
$\angle{\text{A}}=30^{\circ}$
$\text{a}\sin\text{B}=\text{b}\sin\text{A}$
$\Rightarrow2\sin45=\text{b}\sin30$
$\Rightarrow{2}\times\frac{1}{\sqrt{2}}=\text{b}\sin30$
$\Rightarrow2\times\frac{1}{\sqrt{2}}=\text{b}\times\frac{1}{2}$
$\Rightarrow{}\sqrt{2}=\frac{\text{b}}{2}$
$\Rightarrow\text{b}=2\sqrt{2}$

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