A) right angled, but need not be isosceles
B) right angled and isosceles
C) isosceles, but need not be right angled
D) equilateral
Correct Answer: A
Solution :
Given, \[{{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C=2\] \[\Rightarrow \] \[1-{{\cos }^{2}}A+1-{{\cos }^{2}}B+1-{{\cos }^{2}}C=2\] \[\Rightarrow \] \[1={{\cos }^{2}}A+{{\cos }^{2}}B+{{\cos }^{2}}C\] \[\Rightarrow \] \[1=1-2\cos A\,\cos B\,\cos C\] \[\Rightarrow \] \[\cos A\,\cos B\,\cos \,C=0\] At least one angle should be \[{{90}^{o}}\] and sum of two angles should be \[{{90}^{o}}\]. Hence, option [a] is correct.
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