The given situation is represented in the right triangle above, x is the length of the kite string.
To find x (hypotenuse) use the next trigonometric ratio for angle 67º:
[tex]cos67º=\frac{100ft}{x}[/tex]Solve x:
[tex]\begin{gathered} x*cos67º=100ft \\ x=\frac{100ft}{cos67º} \\ \\ x\approx255.93ft \end{gathered}[/tex]Then, the length of the kite string is 255.93 feet