SOLUTION: A kite is flying on 170 feet of string. How high is it above the ground if its height is 82 feet more than the horizontal distance from the person flying​ it? Assume the string i

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Question 1185801: A kite is flying on 170 feet of string. How high is it above the ground if its height is 82 feet more than the horizontal distance from the person flying​ it? Assume the string is being released at ground level.
The kite is _____ feet above ground.

Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The kite is _____ feet above ground.
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Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The information describes a right triangle with legs x (along the ground) and x+82 (the height above the ground) and a hypotenuse (the kite string) of 170.

Use the Pythagorean Theorem: c%5E2=a%5E2%2Bb%5E2

x%5E2%2B%28x%2B82%29%5E2=170%5E2

That gives a quadratic equation that you can solve to find x and then find the height.

The numbers are large enough that solving by factoring, or even using the quadratic formula, is messy. I would graph the two functions x%5E2%2B%28x%2B82%29%5E2%29 and 170%5E2 with a graphing calculator and find where they intersect.

graph%28400%2C400%2C-20%2C100%2C-5000%2C50000%2Cx%5E2%2B%28x%2B82%29%5E2%2C170%5E2%29

The graphs intersect at x=72, so

ANSWER: the height of the kite is 72+82=154 feet