#### Answer

$tan(2\theta) = \frac{24}{7}$

#### 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 $\sqrt{5^2-3^2} = 4$
From part (a), we know that $cos(2\theta) = -\frac{7}{25}$
From part (b), we know that $sin(2\theta) = -\frac{24}{25}$
We can find $tan(2\theta)$:
$tan(2\theta) = \frac{sin(2\theta)}{cos(2\theta)}$
$tan(2\theta) = \frac{-\frac{24}{25}}{-\frac{7}{25}}$
$tan(2\theta) = \frac{24}{7}$