To find the height of the kite, we can use trigonometry. The angle of elevation and the length of the string give us a right triangle, where the string acts as the hypotenuse, the height of the kite is the opposite side, and the distance on the ground (which we don't need for this problem) is the adjacent side.
We can use the sine function, which relates the angle to the opposite and hypotenuse:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here, \(\theta\) is 68 degrees, the opposite side is the height of the kite (\(h\)), and the hypotenuse is the length of the string (1,890 feet). Thus:
\[ \sin(68^\circ) = \frac{h}{1890} \]
To find \(h\), we rearrange the equation:
\[ h = 1890 \cdot \sin(68^\circ) \]
Now we calculate \(\sin(68^\circ)\):
\[ \sin(68^\circ) \approx 0.9272 \quad (\text{using a calculator}) \]
Now we can substitute this value into our equation for \(h\):
\[ h \approx 1890 \cdot 0.9272 \approx 1755.768 \]
Rounding to the nearest whole number, the approximate height of the kite is:
\[ \boxed{1756} \text{ feet} \]