Question

Suppose the angles of a triangle $ABC$ are in $A.P$ and sides $b$ and$c$ satisfy $b:c=\sqrt{3}:\sqrt{2}$ then the angle $A$ equals ?

• A. ${30}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

Answer: (A)

${30}^o$

$\angle A+\angle B+\angle C={180}^o$

$2\angle B=\angle A+\angle C$

$\frac{b}{c}=\frac{\sqrt{3}}{\sqrt{2}}$

$3\angle B={180}^o$

$\angle B={60}^o$

$\frac{\sin A}{a}=\frac{sinb}{b}=\frac{\sin c}{c}$

$\frac{\sin A}{a}=\frac{\sqrt{3}\sqrt{2}}{2\sqrt{3}c}=\frac{\sin c}{\sqrt{2}c}$

$\sin c=1$

$c={90}^o$

$90+60+x={180}^o$

$x={30}^o$.