Final answer:
The horizontal distance from Karen to the projection of the kite on the ground is found using the Pythagorean theorem, and it is approximately 63.8 feet. Since this value does not match any of the provided options, it's likely an issue with the options or rounding is expected.
Step-by-step explanation:
The question asks to find the horizontal distance from Karen to the projection of the kite on the ground. We can form a right-angled triangle with the kite, the point where the kite is directly above, and Karen. Given the kite's altitude is 80 feet and Karen is holding the kite 3 feet above the ground, the vertical distance from her hand to the kite is 80 - 3 = 77 feet. With the string being the hypotenuse at 100 feet in length, we can use the Pythagorean theorem to solve for the horizontal distance (x).
To find the horizontal distance (x), we have:
x² + 77² = 100²
x² = 100² - 77²
x² = 10000 - 5929
x² = 4071
x = sqrt(4071)
x ≈ 63.8
Since none of the options match this value, it's likely that there was a typo in the choices, or we are expected to round to the closest provided option.