Question 818223
{{{drawing(400,400,-5,42,-5,42,

line(0,0,0,5),line(0,5,32.1394,38.3022),
green(line(0,5,32.1394,5),line(32.1394,0,32.1394,38.3022)),
line(-10,0,100,0),locate(-1.5,5.5,H),locate(32.5,5.5,J),locate(33,39,K),
locate(-1.5,3.1,5),locate(32.5,3.1,5),locate(13,22,50) ,
red(arc(0,5,10,-10,0,50)),locate(5,8,"50°") 
 )}}}
<pre>
The kite is at point K.  Your hand is at point H.

I will assume you are holding the string 5 feet above the ground
at point H.  If that's not your height change it to your height.

We want to find JK and then we'll add 5 feet to that.

JK is the opposite side of the 50° angle in right triangle HJK.  
The kite string HK = 50 feet is the hypotenuse of right triangle HJK.

The trig ratio that involves the opposite side and the hypotenuse
is the sine, which is {{{OPPOSITE/HYPOTENUSE}}}

sin(50°) = {{{JK/HK}}}

sin(50°) = {{{JK/50}}}

Multiply both sides by 50

50sin(50°) = JK

50(.7660444431) = JK
38.30222216 = JK

So adding your holding height, (between J and the ground, which is
also 5 feet, gives 43.30222216 feet.  Round to however many decimal
places you were told to round.  To the nearest foot is 43 feet.

Edwin</pre>