In A B C, if a=16, b=24 and c=20, then B 2 = - Vidyadip

MCQ

In $\triangle A B C$, if $a=16, b=24$ and $c=20$, then $\cos \frac{B}{2}=$

✓
$\frac{3}{4}$
B
$\frac{1}{4}$
C
$\frac{1}{2}$
D
$\frac{1}{3}$

✓

Answer

Correct option: A.

$\frac{3}{4}$

(A) $2 s=a+b+c=16+24+20=60 \Rightarrow s=30$
$\therefore \quad \cos \frac{B}{2}=\sqrt{\frac{s(s-b)}{a c}}=\sqrt{\frac{30 \times 6}{320}}=\frac{3}{4}$

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