SOLUTION: Grady is flying a kite on 50 ft of string of string. Its vertical distance from his hand is 10 ft more than the horizontal distance from his hand. Assuming that the string is being

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Question 900875: Grady is flying a kite on 50 ft of string of string. Its vertical distance from his hand is 10 ft more than the horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find its horizontal distance from Grady and its vertical distance from the ground.
Answer by lwsshak3(11628) (Show Source):
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Grady is flying a kite on 50 ft of string of string. Its vertical distance from his hand is 10 ft more than the horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find its horizontal distance from Grady and its vertical distance from the ground.
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Draw a right triangle as follows:
x=horizontal distance from his hand (horizontal leg)
x+10=vertical distance from his hand (vertical leg)
50 ft=hypotenuse
by the pythagorean theorem:
x^2+(x+10)^2=50^2
x^2+x^2+20x+100=2500
2x^2+20x-2400=0
x^2+10x-1200=0
(x+40)(x-30)=0
x=-40 (reject)
or
x=30
x+10+5=45
horizontal distance from Grady=30 ft
vertical distance from the ground=45 ft