Answer
$tan~\frac{x}{2} = 0.5$
Work Step by Step
If $0 \lt x \lt \frac{\pi}{2}$, then the angle $x$ is in quadrant I.
If $sin~x = 0.8$, then $cos~x = \sqrt{1-sin^2~x} = 0.6$
We can find the value of $tan~\frac{x}{2}$:
$tan~\frac{x}{2} = \frac{sin~x}{1+cos~x}$
$tan~\frac{x}{2} = \frac{0.8}{1+0.6}$
$tan~\frac{x}{2} = \frac{0.8}{1.6}$
$tan~\frac{x}{2} = 0.5$
