Question

In $△ABC,$ sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively. If $b=c\sin B,$ then the triangle is

• A. Equilateral
• B. Right angled
• C. Acute angle
• D. Obtuse angle

Answer 1

The correct option is B Right angled

Using sine rule , we have : $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R$
Now, $b=c\sin B$
$\Rightarrow 2R\sin B=2R\sin C\sin B\Rightarrow \sin C=1\therefore \angle C={90}^{\circ }$
So, $△ABC$ is a right angled triangle.