Answer:
45 feet
Step-by-step explanation:
Let x be the distance of Stephanie from the point on the ground
Height of kite=[tex]2x-11[/tex]
Length of string=53 feet
Pythagoras theorem
[tex](Hypotenuse)^2=(Base)^2+(Perpendiculars\;side)^2[/tex]
By using Pythagoras theorem
[tex]AC^2=AB^2+BC^2[/tex]
[tex](53)^2=x^2+(2x-11)^2[/tex]
[tex]x^2+4x^2+121-44x=2809[/tex]
[tex]5x^2-44x+121-2809=0[/tex]
[tex]5x^2-44x-2688=0[/tex]
[tex]5x^2-140x+96x-2688=0[/tex]
[tex]5x(x-28)+96(x-28)=0[/tex]
[tex](x-28)(5x+96)=0[/tex]
[tex]x-28=0\implies x=28[/tex]
[tex]5x+96=0[/tex]
[tex]5x=-96[/tex]
[tex]x=-\frac{96}{5}[/tex]
It is not possible because distance cannot be negative.
x=28 feet
Substitute the value of x
Height of kite above the ground=2(28)-11=45 feet
Therefore,height of kite from the ground=45 feet
