Question

Mark the correct alternative in each of the following: 

In a ∆ABC, if a = 2, \[\angle B = 60°\]  and\[\angle C = 75°\] 

 

Options

• \[\sqrt{3}\] 

• \[\sqrt{6}\]

• \[\sqrt{9}\] 

• \[1 + \sqrt{2}\] 

Answer 1

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).