SOLUTION: Hello all, I have tried to solve this problem but have had no such luck and have not found anything similar to replicate the problem, so any and all help would be appreciated! Not

Question 806463: Hello all, I have tried to solve this problem but have had no such luck and have not found anything similar to replicate the problem, so any and all help would be appreciated! Not really sure how the Pythagorean theorem is supposed to solve this??
I was told that I need to draw a diagram and use the Pythagorean theorem to solve this problem:
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.
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
the Pythagorean theorem is about right triangles. 65 ft is the hypotenuse. vertical distance v=2h-10
a^2+b^2=c^2
v=2h-10,
h^2+v^2=65^2
h = 33, v = 56

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
-------
Right!
Draw a right triangle.
The hypotenuse is 65
The base is "x".
The height is 2x-10.
------
Use Pythagoras to solve for "x":
x^2 + (2x-10)^2 = 65^2
x^2 + 4x^2 - 40x + 100 = 4225
----
5x^2 - 40x - 4125 = 0
Divide thru by 5 to get:
x^2 - 8x - 825 = 0
====
Factor:
(x-33)(x+25) = 0
----
Positive solution:
x = 33 ft (the horizontal distance)
2x-10 = 66-10 = 56 ft (the vertical distance)
===========================
Cheers,
Stan H.
==================
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