Question 548849
Let {{{x}}} be the horizontal distance between the person flying the kite (or more precisely the hand holding the kite string), and the point directly below the kite. 
Then, the height of the kite above the ground is{{{2x-4}}}
We have to assume that the hand holding the string is at the same level as the ground directly below the kite. Then it would look like this:
{{{drawing(200,300,-8,40,-5,67,
triangle(0,0,32,0,32,60), rectangle(30,0,32,2),
locate(8,3.5,horizontal),locate(15,0,x),locate(32.5,30,2x-4),locate(32.5,62,kite),locate(-7.5,2,hand),locate(10,30,68)
)}}} and we would apply Pythagoras theorem to state that {{{x^2+(2x-4)^2=68^2}}}
We simplify the equation to get
{{{x^2+4x^2-16x+16=4624}}} --> {{{5x^2-16x-4608=0}}}
The quadratic formula gives us
{{{x = (16 +- sqrt(16^2-4*5*(-4608)))/(2*5)=(16 +- sqrt(256+92160))/10=(16 +- sqrt(92416))/10=(16 +- 304)/10}}}
We discard the negative solution, because distances are always positive numbers.
So {{{x=(16+304)/10=320/10=32}}}
And rhe height of the kite is
{{{2x-4=2*32-4=64-4=60}}}