The height of the kite will be 6.6 ft rounded to the nearest tenth.
Explanation
According to the below diagram, AB is the height of the kite and AC is the 12 ft line attached to it.
The line is pulled taut and casts a 10 ft shadow. That means BC = 10 ft
Now, in right angle triangle ABC, using Pythagorean theorem....
[tex](AB)^2 +(BC)^2 = (AC)^2 \\ \\ (AB)^2 +(10)^2 = (12)^2 \\ \\ (AB)^2 +100 = 144\\ \\ (AB)^2 = 144-100 =44\\ \\ AB=\sqrt{44}= 6.6332....[/tex]
So, the height of the kite will be 6.6 ft rounded to the nearest tenth.
