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

Answer: (C)

Given, $sinAsinB=\frac{ab}{c^2}$

$\Rightarrow c^2=\frac{ab}{sinAsinB}=\left(\frac{a}{sinA}\right)\left(\frac{b}{sinB}\right)$

$\Rightarrow c^2={\left(\frac{c}{sinc}\right)}^2\left(\because \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinc}\right)$

$\Rightarrow si{n}^{2}C=1$

$\Rightarrow C=90^{\circ }$

Hence, $\Delta ABC$ is a right angled triangle