In triangle A B C, if A B=a b c^2 , then the triangle is - Vidyadip

MCQ

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

A
Equilateral
B
Isosceles
✓
Right angled
D
Obtuse angled

✓

Answer

Correct option: C.

Right angled

(C) $\sin A \sin B =\frac{ ab }{ c ^2}$
$\Rightarrow \sin A \sin B =\frac{( k \sin A )( k \sin B )}{ k ^2 \sin ^2 C }$
$\Rightarrow \sin ^2 C=1 \Rightarrow \sin C=1 \quad \ldots[\because \sin C \neq-1]$
$\begin{array}{l}\Rightarrow \angle C =90^{\circ} \\ \Rightarrow \triangle ABC \text { is right angled. }\end{array}$

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