Question

a kite flying in the air has an 11 - ft line attached to it. its line is pulled taut and casts a 9 - 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 $a = 9$ ft and the length of the kite - string be $c=11$ ft. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$, so $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 9$ and $c = 11$ into the formula: $h=\sqrt{11^{2}-9^{2}}=\sqrt{(11 + 9)(11 - 9)}=\sqrt{20\times2}=\sqrt{40}$.

Step3: Calculate the square - root

$\sqrt{40}\approx6.3$ (rounded to the nearest tenth).

Answer:

$6.3$ ft