Question

a kite flying in the air has a 12 - ft line attached to it. its line is pulled taut and casts a 10 - ft shadow. find the height of the kite. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the kite be $h$, the length of the shadow be $a = 10$ and the length of the line be $c=12$. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$, so $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 10$ and $c = 12$ into the formula: $h=\sqrt{12^{2}-10^{2}}=\sqrt{144 - 100}=\sqrt{44}$.

Step3: Simplify and round

$\sqrt{44}\approx6.6$. Rounding to the nearest tenth, $h\approx6.6$ ft.

Answer:

$6.6$ ft