48.5 feet
1) Sketching this we have:
2) As the point here is how much string was left out, then let's use a trigonometric ratio to find out that hypotenuse since height is always perpendicular (90º with the ground).
[tex]\begin{gathered} \sin (68)=\frac{opposite}{\text{hypotenuse}}=\frac{45}{x} \\ \sin (68)=\frac{45}{x} \\ x\sin (68)=45 \\ \frac{x\sin(68)}{\sin(68)}=\frac{45}{\sin (68)} \\ x=48.53\approx48.5 \end{gathered}[/tex]3) Hence, that kite's string is 48.5 feet long
