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Question
If in ∆ABC, ∠C = 105°, ∠B = 45° and a = 2, then find b.
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Solution
\[ \therefore A = \pi - \left( B + C \right)\]
\[ \Rightarrow A = 180° - \left( 45° + 105° \right) = 30° \]
\[\text{ Now }, \]
\[\text{ According to sine rule }, \frac{a}{sinA} = \frac{b}{sinB} . \]
\[ \Rightarrow \frac{2}{\sin30° } = \frac{b}{\sin45° } \left( \because a = 2, \angle B = {45}^° \right)\]
\[ \Rightarrow \frac{2}{\frac{1}{2}} = \frac{b}{\frac{1}{\sqrt{2}}}\]
\[ \Rightarrow 4 \times \frac{1}{\sqrt{2}} = b\]
\[ \Rightarrow b = 2\sqrt{2}\]
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