Question

a kite flying in the air has a 12 - ft line attached to it. its line is pulled taut and casts an 11 - 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 $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 12$ (the length of the kite - line) and $a = 11$ (the length of the shadow), and $b=h$. So $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 12$ and $a = 11$ into the formula: $h=\sqrt{12^{2}-11^{2}}=\sqrt{144 - 121}=\sqrt{23}$.

Step3: Calculate and round

$\sqrt{23}\approx4.8$ (rounded to the nearest tenth).

Answer:

$4.8$