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  • If in a triangle ABC, then angle  C is equal to ?<div class='qna-op

If in a triangle ABC,(s-a)(s-b)=s(s-c) then angle  C is equal to ?

Option: 1

\frac{\pi}{4}


Option: 2

\frac{\pi}{2}


Option: 3

\frac{3\pi}{4}


Option: 4

None of these


Answers (1)

best_answer

 

 

Half-Angle Formula (in terms of perimeter and sides of triangle)(part 2) -

Half-Angle Formula (in terms of perimeter and sides of triangle)(part 2)

 

\\\mathrm{\tan\frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{s(s-a)}}}\\\\\mathrm{\tan\frac{B}{2}=\sqrt{\frac{(s-a)(s-c)}{s(s-b)}}}\\\\\mathrm{\tan\frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}}

 

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\tan \frac{C}{2} =\sqrt{\frac{ (s-a)(s-b)}{s(s-c)}}\ \ \because (s-a)(s-b)=s(s-c)\\ \tan \frac{C}{2}=1=\tan \frac{\pi}{4}\\ C=\frac{\pi}{2}

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vishal kumar

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