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Question
Mark the correct alternative in each of the following:
In a ∆ABC, if a = 2, \[\angle B = 60°\] and\[\angle C = 75°\]
Options
\[\sqrt{3}\]
\[\sqrt{6}\]
\[\sqrt{9}\]
\[1 + \sqrt{2}\]
Solution
It is given that a = 2, \[\angle B = 60°\] and \[\angle C = 75°\] In ∆ABC, \[\angle A + \angle B + \angle C = 180° \left( \text{ Angle sum property } \right)\]
\[ \Rightarrow \angle A + 60° + 75° = 180°\]
\[ \Rightarrow \angle A = 180° - 135° = 45°\]
Using sine rule, we get
\[\frac{2}{\sin45°} = \frac{b}{\sin60°} \left( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \right)\]
\[ \Rightarrow b = \frac{2 \times \frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}} = \sqrt{6}\]
Hence, the correct answer is option (b).
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