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In a triangle ABC, if sin A sin B= (ab)/...

In a triangle ABC, if sin A `sin B= (ab)/(c^(2))`, then the triangle is :

A

Equilateral

B

Isosceles

C

Right angled

D

Obtuse angled

Text Solution

Verified by Experts

The correct Answer is:
C
`sin A sin B=(ab)/(c^(2)) rArr sin A sin B =((k sin A)(k sin B))/(k^(2) sin^(2) C)`
`rArr sin^(2) C=1 rArr sin C=1`
`rArr c=pi/2 [therefore sin C ne -1] rArr angleC=90^(@), triangle` is right angled.
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