Question

type the correct answer in the box. write your answer to two decimal places.
a youth group is setting up camp. rain is predicted, so the campers decide to build a fly, or rain cover, over their tent. the fly will be 12 feet high and 16 feet wide. the scouts are building the frame for the fly with two poles slanted and joined together at the top of the tent.
the minimum length of the slanted poles needed to support the fly is □ feet.

Explanation:

Step1: Identify the triangle type

The tent's cross - section is a triangle. The height of the triangle (vertical side) is 12 feet, and half of the base (since the total width is 16 feet) is $\frac{16}{2}=8$ feet. The slanted pole forms the hypotenuse of a right - triangle with legs 12 feet and 8 feet.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c = \sqrt{a^{2}+b^{2}}$. Here, $a = 12$ and $b = 8$. So we calculate $c=\sqrt{12^{2}+8^{2}}=\sqrt{144 + 64}=\sqrt{208}$.

Step3: Simplify and round

$\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}\approx4\times3.6055 = 14.422$. Rounding to two decimal places, we get 14.42.

Answer:

14.42