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A boy is flying a kite. The height of the kite is 1 and 1/2 times greater than the...

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A boy is flying a kite. The height of the kite is 1 and 1/2 times greater than the horizontal distance (x).  The length of the string that is out is 520 ft.  Determine the height of the kite.  

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The boy is flying a kite. The height of the kite is 1.5 times greater than the horizontal distance. The length of the string attached to the kite is 520 ft.

A right triangle is formed by the string, the vertical line along the height of the kite and the horizontal distance of the kite. Let the horizontal distance be x, the height of the kite is 1.5*x. Using the Pythagorean Theorem,

x^2 + (1.5*x)^2 = 520^2

=> x^2*3.25 = 520^2

=> x `~~` 288.44 ft.

The height of the kite is 432.7 ft.

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