Question

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

• A. ${90}^o$
• B. ${45}^o$
• C. ${30}^o$
• D. ${60}^o$

Answer 1

The correct option is A ${90}^o$

We have,

$(s-a)(s-b)=s(s-c)$

$\frac{(s-a)(s-b)}{s(s-c)}=1$

${\tan }^2\frac{C}{2}=1$

${\tan }^2\frac{C}{2}={\tan }^2\frac{\pi }{4}$

$C=\frac{2\pi }{4}$

$C=\frac{\pi }{2}$

$C={90}^o$

Hence, this is the answer.