Question

Angles A, B, and C of a triangle \(\Delta ABC\) are in AP and \( b:c = \sqrt{3} : \sqrt{2} \), then angle \( \angle A \) is given by

• A. 45°
• B. 60°
• C. 75°
• D. 90°

Answer 1

The Correct Option is C

Since angles are in AP: \[ A = x - d,\quad B = x,\quad C = x + d \Rightarrow A + B + C = 180^\circ \Rightarrow 3x = 180 \Rightarrow x = 60^\circ \] So: \[ A = 45^\circ,\quad B = 60^\circ,\quad C = 75^\circ \] Use sine rule: \[ \frac{b}{\sin B} = \frac{c}{\sin C} \Rightarrow \frac{b}{\sin 60^\circ} = \frac{c}{\sin 75^\circ} \Rightarrow \frac{\sqrt{3}}{\sqrt{3}/2} = \frac{\sqrt{2}}{\sin 75^\circ} \Rightarrow \text{Only possible when } A = 75^\circ \]