Question

In a triangle $ABC,\angle B=\frac{\pi }{2},$ if $s-a=10$ and $s-c=3,$ then $△=$

• A. $15$
• B. $30$
• C. $24$
• D. $36$

Answer 1

The correct option is B $30$

$\tan \frac{B}{2}=\tan \frac{\frac{\pi }{2}}{2}=\tan \frac{\pi }{4}=1$
$\Rightarrow \tan \frac{B}{2}=\frac{(s-c)(s-a)}{△}=1$
$\Rightarrow (s-c)(s-a)=△$
$\therefore △=(s-c)(s-a)=3\times 10=30$