# In a ∆ABC, if sin2 A + sin2 B = sin2 C, show that the triangle is right angled.

Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get  So by considering the given condition, we get

sin2 A + sin2 B = sin2 C

Substituting the values from equation (i), we get   This is Pythagoras theorem; hence the given triangle ABC is right - angles triangle

Hence proved

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