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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If in a triangle $A B C,(s-a)(s-b)=s(s-c)$, then angle $C$ is equal to
  • ✓
    $90^{\circ}$
  • B
    $45^{\circ}$
  • C
    $30^{\circ}$
  • D
    $60^{\circ}$
✓

Answer

Correct option: A.
$90^{\circ}$
(A) $\tan \frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=1$
$\Rightarrow \tan \frac{ C }{2}=\tan 45^{\circ} \Rightarrow \frac{ C }{2}=45^{\circ}$
$\Rightarrow C=90^{\circ}$

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