#### Answer

$sin(2\theta) = -\frac{24}{25}$

#### Work Step by Step

If $90^{\circ} \lt \theta \lt 180^{\circ}$, then the angle $\theta$ is in quadrant II.
If the hypotenuse is 5, and the adjacent side has a length of 3, then the length of the opposite side is $\sqrt{5^2-3^2} = 4$
$sin(2\theta) = 2~sin~\theta~cos~\theta$
$sin(2\theta) = (2)(\frac{4}{5})(-\frac{3}{5})$
$sin(2\theta) = -\frac{24}{25}$