A pythagorean question?

Question

a kite is flying on 50ft of string. its vertical distance from the groung is 10ft more than its horizontal distancefrom the person flying it. assuming that the string is being held at groung level, find it horizotal distance from the person and its vertical distance from the ground

Answer 1

Let the horizontal distance be x.  Then, the vertical distance is x + 10, and so we have a right triangle with legs x and x + 10 and hypotenuse 50.  Therefore, by the Pythagorean Theorem:

x^2 + (x + 10)^2 = 2500

2x^2 + 20x - 2400 = 0

x^2 + 10 x - 1200 = 0

(x - 30)(x + 40) = 0

x = 30

So the horizontal distance is 30 and the vertical distance is 40.

Answer 2

One could figure this out the hard way, but one can also note that the most basic pythagorean triple of integers is 3, 4, and 5; a similar triangle with a 50 ft hypotenuse is 30, 40, 50, and 40 is 10 greater than 30.

So the answer is that the horizontal distance is 30 ft and the vertical distance is 40 ft.