Question 1147588
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Of course, in the real world the string from the kite flier to the kite would not be a straight line....<br>
But for the purposes of the problem, suppose it is.  Then the horizontal and vertical distances and the string form a right triangle.<br>
Algebraically, then, by the Pythagorean Theorem,<br>
{{{x^2 + (x+4)^2 = 20^2}}}<br>
You can continue from there to solve the problem algebraically if needed.<br>
But with a little experience with this kind of problem, you might notice that a hypotenuse of 20 might be a "scale model" of a right triangle with a hypotenuse of 5 -- a 3-4-5 right triangle.<br>
The scale model would be 12-16-20; and those lengths satisfy the given condition that the hypotenuse is 20 and the length of one leg is 4 more than the length of the other.<br>
ANSWER: horizontal distance 12 feet; vertical distance 16 feet.<br>