Question

In triangle $ABC$, if $b=3,c=4$ and $\angle B=\pi /3$, then numbers of such triangles is -

• A. $1$
• B. $2$
• C. $0$
• D. $infinite$

Answer 1

Answer: (C)

$0$

According to question,

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$⟹\cos \frac{\pi }{3}=\frac{a^2+16-9}{8a}$

$⟹\frac{1}{2}=\frac{a^2+7}{8a}$

$⟹a^2-4a+7=0$

Discriminant(D) of this quadratic is negative ( $D=16-28=-12$)

so, $0$ no. of triangle forms.