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 be $h$, hypotenuse $c=12$, base $b=10$. The theorem is $h^2 + b^2 = c^2$. Rearrange to solve for $h$:
$h = \sqrt{c^2 - b^2}$

Step2: Substitute values into formula

Substitute $c=12$, $b=10$:
$h = \sqrt{12^2 - 10^2} = \sqrt{144 - 100} = \sqrt{44}$

Step3: Calculate and round result

$\sqrt{44} \approx 6.6$

Answer:

6.6 ft