If in a triangle the angles are in A. P. and b: c=3: 2, then A is… - Vidyadip

MCQ

If in a triangle the angles are in A. P. and $b: c=\sqrt{3}: \sqrt{2}$, then $\angle A$ is equal to

A
$30^{\circ}$
B
$60^{\circ}$
C
$15^{\circ}$
✓
$75^{\circ}$

✓

Answer

Correct option: D.

$75^{\circ}$

(D) Since the angles are in A.P., therefore $B =60^{\circ}$ By sine rule,
$\frac{b}{c}=\frac{\sin B}{\sin C} \Rightarrow \frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{3}}{2 \sin C} \Rightarrow C=45^{\circ}$
$\therefore \quad A=180^{\circ}-60^{\circ}-45^{\circ}=75^{\circ}$

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