To find the approximate height of the kite given the angle of elevation and the length of the string, you can use trigonometric functions. In this case, you can use the sine function because it relates the opposite side, which is the height of the kite, to the hypotenuse, which is the length of the string.
Let \( h \) represent the height of the kite. The sine of the angle of elevation (\( \theta = 68^\circ \)) is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{\text{length of the string}} \]
In this case, the hypotenuse is the string length (1890 feet). Therefore, we can rearrange the equation to solve for \( h \):
\[ h = \text{length of the string} \times \sin(\theta) \]
Substituting the known values:
\[ h = 1890 \times \sin(68^\circ) \]
Now we calculate \( \sin(68^\circ) \):
\[ \sin(68^\circ) \approx 0.9272 \]
Now plug this value into the equation:
\[ h \approx 1890 \times 0.9272 \approx 1751.77 \]
Thus, the approximate height of the kite is:
\[ \approx 1752 \text{ feet} \]
So, the height of the kite is approximately 1752 feet.
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