Question

a kite is flying 12 ft off the ground. its line is pulled taut and casts a 9 - ft shadow. find the length to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

We have a right - triangle where the height of the kite off the ground is one leg ($a = 12$ ft) and the length of the shadow is the other leg ($b = 9$ ft). We want to find the length of the hypotenuse $c$ (the length of the kite string).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Substitute $a = 12$ and $b = 9$ into the formula: $c^{2}=12^{2}+9^{2}=144 + 81=225$.

Step3: Solve for $c$

Take the square root of both sides: $c=\sqrt{225}=15$ ft.

Answer:

15