Question 806463
Prairie Dawn is flying a kite on 65 feet of string. Its vertical distance from the ground is 10 feet less than twice its horizontal distance from Prairie Dawn. Assuming that the string is being held at ground level, find its horizontal distance from Prairie Dawn and its vertical distance from the ground.
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Right!
Draw a right triangle.
The hypotenuse is 65
The base is "x".
The height is 2x-10.
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Use Pythagoras to solve for "x":
x^2 + (2x-10)^2 = 65^2
x^2 + 4x^2 - 40x + 100 = 4225
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5x^2 - 40x - 4125 = 0
Divide thru by 5 to get:
x^2 - 8x - 825 = 0
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Factor:
(x-33)(x+25) = 0
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Positive solution:
x = 33 ft (the horizontal distance)
2x-10 = 66-10 = 56 ft (the vertical distance)
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Cheers,
Stan H.
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