Answer
Positive
Work Step by Step
$180 < A < 270$
Dividing by 2
$90 < \dfrac{A}{2} < 135$
$\therefore \dfrac{A}{2} $ terminates in $QII$
$\because$ The sine of an angle in $QII$ is positive.
$\therefore \sin{\dfrac{A}{2}}$ is positive.