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A kite is flying on 181 feet of string. How high is it above the ground if its height is 161 feet more than the horizontal distance from the person flying it? Assume the string is being released at ground level.

Answer :

Final Answer:

The kite is flying at a height of approximately 268 feet above the ground, given a string length of 181 feet and a height difference of 161 feet from the horizontal distance.

Explanation:

To determine the height of the kite above the ground, we can use the Pythagorean theorem since the string, the height, and the horizontal distance form a right triangle. The given information states that the length of the string (hypotenuse) is 181 feet and that the height of the kite is 161 feet more than the horizontal distance.

Let h represent the height of the kite above the ground, and d represent the horizontal distance from the person flying it. According to the given information, we have the equation:

h = d + 161

Now, using the Pythagorean theorem:

[tex]\[h^2 + d^2 = \text{string length}^2\][/tex]

[tex]\[(d + 161)^2 + d^2 = 181^2\][/tex]

Solving for d using the quadratic equation yields d ≈ 62.42 feet. Then, substituting this value back into h = d + 161, we find h ≈ 223.42 feet. Rounding to the nearest foot, the kite is flying approximately 268 feet above the ground.

In essence, this problem showcases the application of geometry and the Pythagorean theorem to determine the height of the kite using given information about the string length and the relationship between the height and horizontal distance.

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