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, $sin \,A \,sin \,B = \frac{ab}{c^{2}}$

$\Rightarrow c^{2}=\frac{ab}{sin\,A\,sin\,B}=\left(\frac{a}{sin\,A}\right)\left(\frac{b}{sin\,B}\right)$

$\Rightarrow c^{2}=\left(\frac{c}{sin\,c}\right)^{2} \left(\because\, \frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,c}\right)$

$\Rightarrow sin^{2} C=1$

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

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