Question

In a triangle $ABC$, if $\sin A\sin B=\frac{ab}{c^2}$, then the triangle is

• A. Equilateral
• B. Isosceles
• C. Right angled
• D. Obtuse angled

Answer 1

The correct option is C Right angled

Given, $\sin A\sin B=\frac{ab}{c^2}$
$\Rightarrow c^2=\frac{ab}{\sin A\sin B}=\left(\frac{a}{\sin A}\right)\left(\frac{b}{\sin B}\right)$
$\Rightarrow c^2={\left(\frac{c}{\sin C}\right)}^2(\because \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C})$
$\Rightarrow {\sin }^{2}C=1$
$\Rightarrow C={90}^{}$
Hence, $\Delta ABC$ is a right angled triangle.