Question

If in a $\Delta$ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find $sin\left(\frac{A}{2}\right)$.

• A. $\frac{1}{\sqrt{5}}$
• B. $\sqrt{5}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

The correct option is A $\frac{1}{\sqrt{5}}$

We know, $sin\left(\frac{A}{2}\right)=\sqrt{\frac{(s-b)(s-c)}{b.c}}$
Where"s" is the semiperimeter and b & c are the sides of a triangle.
We'll do the appropriate substitution -
$sin\left(\frac{A}{2}\right)=\sqrt{\frac{(6-3)(6-5)}{3.5}}$
$sin\left(\frac{A}{2}\right)=\frac{1}{\sqrt{5}}$