Question

In 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 A Equilateral

$\begin{array}{cc}& \begin{array}{c}\sin A\cdot \sin B=\frac{ab}{c^2}\\ \begin{array}{cc}\Rightarrow \frac{ab}{\sin A\cdot \sin B}=c^2& =\left(\frac{a}{\sin A}\right)\left(\frac{b}{\sin B}\right)\\ & =\left(\frac{c}{\sin c}\right)\left(\frac{c}{\sin c}\right)\end{array}\Rightarrow {\sin }^{2}C=1\end{array}\\ & \Rightarrow C={90}^{\circ }\Rightarrow △ABC\text{is might - angled triangle}\end{array}$