Given that length of the kite string = 80 feet.
Kite always flies above the ground so that can be assumed as kite is making right angle triangle with the ground as shown in the image.
Now we have to find about how far is the child from the stop sign. To find that we can apply Pythagorean theorem.
[tex] (Hypotenuse)^2=(Base)^2+(Perpendicular)^2 [/tex]
[tex] (80)^2=x^2+(35)^2 [/tex]
[tex] 6400=x^2+1225 [/tex]
[tex] 6400-1225 =x^2[/tex]
[tex] 5175=x^2[/tex]
take square root of both sides
[tex] 15 \sqrt{23} =x[/tex]
which is approx 71.94
Hence child is approx 71.94 feet. or to be more accurate [tex] 15 \sqrt{23} [/tex] feet.
