Question

a kite flying in the air has an 11 - 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 $a = 10$ ft and the length of the string be $c=11$ ft. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$.

Step2: Solve for $h$

We can rewrite the Pythagorean - theorem formula to solve for $h$: $h=\sqrt{c^{2}-a^{2}}$. Substitute $a = 10$ and $c = 11$ into the formula: $h=\sqrt{11^{2}-10^{2}}=\sqrt{121 - 100}=\sqrt{21}\approx4.6$ ft.

Answer:

$4.6$ ft