Question:
If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b.
Solution:
We know, $A+B+C=\pi$
$\therefore A=\pi-(\mathrm{B}+\mathrm{C})$
$\Rightarrow A=180^{\circ}-\left(45^{\circ}+105^{\circ}\right)=30^{\circ}$
Now,
According to sine rule, $\frac{a}{\sin \mathrm{A}}=\frac{b}{\sin \mathrm{B}}$.
$\Rightarrow \frac{2}{\sin 30^{\circ}}=\frac{b}{\sin 45^{\circ}} \quad\left(\because a=2, \angle B=45^{\circ}\right)$
$\Rightarrow \frac{2}{\frac{1}{2}}=\frac{b}{\frac{1}{\sqrt{2}}}$
$\Rightarrow 4 \times \frac{1}{\sqrt{2}}=b$
$\Rightarrow b=2 \sqrt{2}$
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